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@hardenedapple
Last active August 29, 2015 14:21
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Definition of \"amplitude\" and \"frequency\" used throughout\n",
"Given the equation for the impurities momentum\n",
"$$ < P_{\\downarrow} > = Q - \\sum e^{i(E(f) - E(f^{'}))t} < FS|f >< f|P_{\\uparrow}|f^{'} >< f^{'}|FS >$$\n",
"define \"frequency\" as $E(f) - E(f^{'})$ and \"amplitude\" of a transition as $ < FS|f >< f|P_{\\uparrow}|f^{'} >< f^{'}|FS > $\n",
"\n",
"# For when the above equations aren't shown properly\n",
"\"frequency\" is E(f) - E(f') \n",
"\n",
"\"amplitude\" is < FS | f > < f | P_background | f_primed > < f_primed|FS >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Premise, and Outline\n",
"\n",
"### Different transitions cause different features\n",
"#### Same-branch transitions cause a flat bottom in \"thermalised\" regime\n",
"#### Different-branch transitions cause the flutter.\n",
"Reminder that those transitions between states in the same branch (e.g. the main branch consists of states with a pseudo hole of either 49 or -50) don't contribute to the flutter.\n",
"\n",
"### No singularity at flutter frequency apparent when looking at all transitions\n",
"Histogram of number of transitions \n",
"Both when looking at the number of transitions there, and the sum of amplitudes in the range we see nothing special\n",
"### Histogram of amplitudes only using _different-branch_ transitions shows peak at flutter frequency\n",
"The amplitudes of the __different-branch__ transitions show a peak at the amplitude frequency.\n",
"This is to be expected, as we know that frequency is seen in their sum.\n",
"### Still no singularity in _number_ of transitions near flutter frequency\n",
"Only looking at __different-branch__ transitions does not make any singularity apparent in the number of states.\n",
"### Amplitude peak gets more pronounced with increasing system size\n",
"For a smaller system, the amplitude peak of inter-branch transitions isn't as clear\n",
"\n",
"### The peak is not from a few very large amplitude transitions\n",
"The fourier transform doesn't show any particularly large amplitudes at this frequency\n",
"\n",
"### It must come from transitions at the flutter frequency having a high _average_ amplitude\n",
"\n",
"\n",
"## Finally, some mention of the \"majority\" contribution\n",
"Transitions to/from states with a pseudo hole on the negative edge of the pseudo Fermi sea, where in the transition the pseudo particle doesn't change, cause most of the flutter\n",
"\n",
"There is a strong peak in these states.\n",
"\n",
"But they don't cause __all__ of the flutter."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Parameters of system\n",
"While I've checked this for multiple different parameters, these plots are only for two different systems\n",
"\n",
"All graphs except those for the specifically mentioned smaller system are for the system with the parameters\n",
"\n",
"N=99\n",
"\n",
"L=297\n",
"\n",
"m_q=66\n",
"\n",
"V=1.0\n",
"\n",
"$\\gamma = 3$\n",
"\n",
"$Q = \\frac{4}{3} k_F$\n",
"\n",
"The smaller system just changes the system size (N=45), $\\gamma$ and $Q / k_F$ are kept constant."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Definition of _different-branch_ and _same-branch_ transitions\n",
"\n",
"On the graph of eigenstate energies against their overlap, there are some parametric families.\n",
"\n",
"I call a __branch__, the set of states which form one line in this graph.\n",
"\n",
"Hence __different-branch__ transitions are transitions between states which are on different branches.\n",
"\n",
"Note, to numerically define these branches, I define them based on how \"deep\" into the pseudo sea their hole is.\n",
"This means the main branch consists of those states with a pseudo hole of either 49 or -50, the second to main branch consists of those states with a pseudo hole of either 48 or -49, etc.\n",
"\n",
"This graph has some examples"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"collapsed": false
},
"outputs": [
{
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BHXdE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\n2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REpijJzLA5mZDNnSwqHUnK4vnoQtcP9CfM3TxVvbNqE9frrMGUKJCf7ijUg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\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xvzc/nwJ2r14BoVunVSuWhTCaFACKr1u2UNANTsBISOB5TifFz2DKy2kk6NnTLIhefDHF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AEWC04ls8Rt+fnsawcCEEewxAQOB7vshdSutlafbNNzdSACwW10CDY1lT0Gnw/EaCikT+DGxGit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\noq8/cgR/wcEQ1flaU7dvx/e3bJHG6uBBlDd7tu+9ZW4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TiKzi69ayiA4d1O0jPx/pK378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Q0G9JnnHO1wuO+AQYR3vs2bxfPTvHkgIaekgPQxeDDa36wZ+sSVjHX6NMjxn3+O34SH471r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\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"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image(filename=\"g9605.png\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Caption\n",
"\n",
"I plot the well known graph of eigenstates here, but I only plot those with a single pseudo excitation for clarity.\n",
"\n",
"In the above graph, the states with pseudo hole of 49, 48, 47, -50, -49, -48 are highlighted in magenta, green, red, cyan, yellow, and black respectively.\n",
"\n",
"By the definition I'm using, the yellow and green states are in the same \"branch\", hence transitions between two states where both are either green or yellow, are __same-branch__ transitions.\n",
"\n",
"Correspondingly, a transition between a states with a pseudo hole of -50 and a state with a pseudo hole of 48 (i.e. a cyan state and a green state) is a __different-branch__ transition."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import itertools as itt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from mcba.models.impurity.ph_param import Par, E_F, k_F, initial_q\n",
"\n",
"# Keep \\gamma as 3 throughout, keep initial momentum at 4/3 k_F\n",
"larger_system = Par(N=99, L=297, m_q=66, V=1.0)\n",
"smaller_system = Par(N=45, L=135, m_q=30, V=1.0)\n",
"\n",
"# Flutter period of 14.8 taken from graphs, frequency \\approx 0.424 E_{F}\n",
"# only looking at systems with this frequency.\n",
"flutter_frequency = 2*np.pi / 14.8"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Ignore this cell\n",
"\n",
"def plot_histogram_from_file(histogram_file, par, limited=False, amplitudes=False,\n",
" ylimits=None, xlimits=None):\n",
" \"\"\"Take precalculated histogram data and plot it.\"\"\"\n",
" totaldata = np.load(histogram_file)\n",
" bar_width = 0.8*totaldata['left_edge'][1]\n",
"\n",
" frequency_edges = totaldata['left_edge'] / E_F(par)\n",
"\n",
" if amplitudes:\n",
" height = totaldata['values'] / k_F(par)\n",
" yname = r'Amplitude $k/k_F$'\n",
" else:\n",
" height = totaldata['values']\n",
" yname = r'Number of transitions'\n",
"\n",
" if limited:\n",
" smaller_filter = np.logical_and(frequency_edges < flutter_frequency + 0.2,\n",
" frequency_edges > flutter_frequency - 0.2)\n",
" height = height[smaller_filter]\n",
" frequency_edges = frequency_edges[smaller_filter]\n",
"\n",
" plt.bar(frequency_edges, height, width=bar_width)\n",
" plt.xlabel(r'Frequency $\\omega/E_F$', fontsize=20)\n",
" plt.ylabel(yname, fontsize=20)\n",
" plt.axvline(flutter_frequency, label='Flutter frequency',c='r')\n",
" if ylimits:\n",
" plt.ylim(ylimits)\n",
" if xlimits:\n",
" plt.xlim(xlimits)\n",
" \n",
" \n",
" plt.show()\n",
"\n",
"\n",
"def same_branch_transitions(database_name, number_of_states, amplitude_store):\n",
" families, par = pf.get_family_eigenstates(database_name, number_of_states)\n",
" edge_val = (par.N - 1) / 2\n",
" \n",
" for val in range(edge_val + 1):\n",
" families[val].extend(families[-(val + 1)])\n",
" \n",
" coords = list(pf.single_family_interactions(families, edge_val, 0))\n",
" for val in range(edge_val):\n",
" coords.extend(pf.single_family_interactions(families, val, 0))\n",
"\n",
" amps = pm.get_part_amps(coords, amplitude_store, number_of_states)\n",
" return amps\n",
"\n",
"\n",
"def plot_fourier_transform(filename, parameters, title, ylimits=None):\n",
" amp_array = np.load(filename)\n",
" amp_array['frequencies'] = abs(amp_array['frequencies'])\n",
" amp_array['frequencies'] /= E_F(parameters)\n",
" amp_array['amplitudes'] /= k_F(parameters)\n",
" smaller_limit = amp_array['frequencies'] < 1\n",
" amp_array = amp_array[smaller_limit]\n",
" plt.scatter(amp_array['frequencies'], amp_array['amplitudes'])\n",
" plt.ylabel(r'Amplitude $k / k_F$', fontsize=20)\n",
" plt.xlabel(r'Frequency $\\omega / E_F$', fontsize=20)\n",
" plt.axvline(flutter_frequency, c='r')\n",
" plt.ylim(ylimits)\n",
" plt.suptitle(title, fontsize=20)\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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8XdLPeg3SaNHXgBeAp7LHY6Tfy0LSz6Pn+2cafwbZqMr1SaMotyf9n3kb6ed8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\nmRXKicXMzArlxGJmZoVyYjEzs0L9f3U1fJ8ie3NsAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72ea2709d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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R+DS9bZrYijpLupwF7Nl0IC26kdKB3/qEpIiYeSRGVmh/Xo2XH0Ppa9nCZlmzkfVPnRbL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\no/4/Na12JTQijYQAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72e8f5a350>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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+fgJwN/By4NvAv+ftnwe+2elYcyyfA84ELszPuy5O4DRgZv5+DDCx2+IEXgLc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\nMzMr1f8B0/QUVcX5W5cAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72ea17b290>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Define the plotting range\n",
"time_lower_bound = 0\n",
"time_upper_bound = 150\n",
"\n",
"# Total Momentum of impurity\n",
"main_data = np.load('Results/new_data/mompts/momentum_pointsN99L297q66V1_00_cache20000.npy')\n",
"smaller_filter = np.logical_and(main_data['time'] < time_upper_bound,\n",
" main_data['time'] > time_lower_bound)\n",
"plotting_points = main_data[smaller_filter]\n",
"plt.plot(plotting_points['time'], plotting_points['momentum'])\n",
"plt.xlabel(r'Time $t/t_F$', fontsize=20)\n",
"plt.ylabel(r'Momentum $k/k_F$', fontsize=20)\n",
"plt.show()\n",
"\n",
"# Contribution from transitions between states in the same branch \n",
"# Here I define a \"branch\" of states by how far from an edge of the pseudo sea the states' pseudo hole is.\n",
"# e.g. the main \"branch\" of states for a N=99 particle system are those states with a pseudo hole of either 49 or -50\n",
"import plotting_functions as pf\n",
"import partial_mom as pm\n",
"database_name = 'Results/new_data/sqlite/N99L297q66V1.00.sqlite'\n",
"amplitude_store = 'Results/new_data/Ordered_amplitude_matrices/N99L297q66V1_00_cache20000.mem'\n",
"number_of_states = 20000\n",
"\n",
"# Here I find all the transitions between states which are in the same branch as each other. \n",
"amps = same_branch_transitions(database_name, number_of_states, amplitude_store)\n",
"amp_array = pm.np_array_from_dict(amps)\n",
"diagonal, _ = pf.diagonal_and_overlap(database_name, number_of_states, lambda val: pf.singly_excited)\n",
"\n",
"fermi_time = 1. / E_F(larger_system)\n",
"timelist = pf.maketimepoints(200, 0, 2, 1000)\n",
"normalised_time = timelist / fermi_time\n",
"# Contribution from all transitions between states in the same branch\n",
"intra_branch_contributions = pf.form_points(amp_array,\n",
" (k_F(larger_system), initial_q(larger_system)),\n",
" timelist,\n",
" diagonal)\n",
"smaller_filter = np.logical_and(normalised_time < time_upper_bound,\n",
" normalised_time > time_lower_bound)\n",
"plotting_time = normalised_time\n",
"normalised_time, intra_branch_contributions = normalised_time[smaller_filter], np.array(intra_branch_contributions)[smaller_filter]\n",
"plt.plot(normalised_time, intra_branch_contributions)\n",
"plt.xlabel(r'Time $t/t_F$', fontsize=20)\n",
"plt.ylabel(r'Momentum $k/k_F$', fontsize=20)\n",
"plt.ylim(0.2, 1.4) # Make same scale as previous\n",
"plt.show()\n",
"\n",
"\n",
"\n",
"# Contribution from transitions between states which don't share a branch\n",
"# i.e. all different-branch transitions\n",
"# Takes more RAM than I have on my laptop, so I run it on the HEC and plot the results here\n",
"inter_transitions_store = 'Results/new_data/inter_family_plotpoints.npy'\n",
"inter_data = np.load(inter_transitions_store)\n",
"smaller_filter = np.logical_and(inter_data['time'] < time_upper_bound,\n",
" inter_data['time'] > time_lower_bound)\n",
"inter_data = inter_data[smaller_filter]\n",
"plt.plot(inter_data['time'], inter_data['momentum'])\n",
"plt.xlabel(r'Time $t/t_F$', fontsize=20)\n",
"plt.ylabel(r'Momentum $k/k_F$', fontsize=20)\n",
"plt.ylim(1.1, 2.3) # Make same scale once shifted\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Caption\n",
"\n",
"Above figures compare total momentum to the contribution from __same-branch__ transitions and from __different-branch__ transitions.\n",
"\n",
"### First figure shows total momentum against time\n",
"\n",
"### Second figure shows _same-branch_ contributions\n",
"The contribution of __same-branch__ transitions shows __no flutter__.\n",
"\n",
"### Third figure _different-branch_ contributions\n",
"The contribution from __different-branch__ transitions is where the flutter comes from.\n",
"\n",
"I use this as justification to limit my graphs to __different-branch__ transitions later on."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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byGCVpwb5Lk306oiIvhwZo50crMys6qoUrMr0BvwiKVBdB1xAmoyxo13XzczM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\nzKzv/X8PfQt7yLXyWAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f11c81020d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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qo0rcecPMzDqmzMgZ53YwDjMzs5ZM+BEuzMxsYnHiMjOzgdLyqUJJDzP29SuR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\nJy4zMxsoTlxmZjZQnLjMzGyg/H+qQh0ZAnaqbgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f11a72be090>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# When plotting the number of states, we see no pattern\n",
"countN99 = 'Results/new_data/histograms/countN99_coarse.npy'\n",
"plot_histogram_from_file(countN99, larger_system)\n",
"plot_histogram_from_file(countN99, larger_system, limited=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Caption\n",
"Histogram of the total number of transitions against frequency.\n",
"\n",
"We see no feature at the flutter frequency (marked in red)"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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sN0h68xifY1b+vSyV9LSkByVdLunt+fod87p/OUYdt0l6VtKWrcpU7N3At9uU\nmU12S4/ragskrSNpw7oyS3sQm/WRW0Y2bF5KdlC6CzgXWB9YASDpMOAbZAeuS8ju3rk9cDjwz5J2\ni4gH6iuT9FXgaOBB4HRgFTAX2JXsVtTN/mMfq297rXVl4gJeDFxPdgOzc4DNyO6vdLGkvSNiQcM+\nPgCcCqzM93EP2Q3NXgd8EPhBfs+eK4A9Jc2MhltqS3o92fmXH0bEsjE+YyUkTQJGgI+MUWYysDtw\nTUSsrFv1dmA5a1pLF/QoTOuXVHcK9MOPiIDsZPRq4ASyu9bWPw6tKzejruxnm9SzPfAscDewVcO6\nvciSzAUNy1+f13c3MLVu+fNZc6L8D3XLR/Jln27xWRbXly8TV8PnPL6h/Jvy5T9pWL4TWRJ6hOZ3\nBn1h3euD8jq+2KTcN/N1/1jg5zYZ+FKbMqcCvxtj/T7AyW3q2D2P6bi6ZZsCvwE2SP3760d1j+QB\n+DGxH3UH3maPX9aVqx2kHwQmN6nnP/P1+7bYz4X5AXvDumVn5Nsc2qT87IqSUUdx1X3OP5APMGoo\n/0fg4YZlJ+fbHFPg+55E1qW1HFi3bvlUsjux3l3w5/YR4JVtypyVx7V5i/VnA7u3qePYvI5rgcvI\nWovPANel/t31o9qHu+lsEERETCpY9pYY3V1Ts3v+PCJp1ybr/47sQLwDUBv+uwtZt9qvmpT/NWuG\nEHejTFwAv438aNzgAbIuxHq75c+XtQsmIp6TdAbZreAPAr6br3oPsB5Zd+KYJK0LTI+GUY6SNo3R\nt5U+mqzL8/EmdawHvDoirm2zu9lkyWd2RDybb3s4MLNdnDZcnIxs2DzUYvlm+fP/HWPbAOpPek/J\nn9c6PxIRqyQ90nl4lcQFTQ7guVWsPfBoal5H0ZP43wCOA45kTTI6guygf3aB7d8E/LR+gaS5eR1/\nG2AREU9KWhARq5rU8Wbg0rF2kp9TegOwsJaIciuAK+vK7QysiIj7C8RuA8qj6WzYtBo8sCJft3FE\nPK/FY1JEXNWwDWQXTo4iaR1g84bFtZZSq3/iplYUV6dqiWubIoUj4kGyQQ5vlLRD3cCFCyPi0QJV\n7E3WXVZvf+DG+gWSZgC3t6jjnbQfRfdqYCOg8btZCPyi7v3/Ajyse8g5Gdl4cS3ZVfhvbFewzo35\nNrObrPsH1v77eCx/flFjYUnbARtXFFenavvYt4NtTsmfjyRr0UA2mrCIGWSDMuq9nLVnUfh3shGP\no0iaAryy8cugAAADKUlEQVQoIu5os5/ad3Z1/cKIuC8ins7regnwRK3rVtJGkuZJelLSjyUdlz8+\nJ+kuSfMKfD5LIfVJKz8m9oOstfFcgXIz8rJntVi/A1k3013AzCbr1wX2aFhWG013D7BJ3fL1yA7w\njQMY1iFrhTwGbFG3fH2yLqdR5cvEVeBzLmj8voCXkSWHR2k+mm6bFnXdmW/zJHBHBz+zHwEH1L0/\nGniOLMFAlsRPBM5ssf1hwMcK7Ocism7JKWOUOb/xewU2ybd7ecPyXYDDU//O+9H84XNGNi5ExF35\n9TxnAbdL+ilZkplM1pLZg+zc0E5121wj6WSyg+nvJJ1PNrJtLtlB+k8N+1iVX5d0PHCzpIvIEtTe\nZOdrHiRroXQVVwGN+1gk6UPAaXlcFwP3kp2v+nuyrsK9mtRzGvDl/HXbgQt1bgTOkXRB/hl2Imu9\nzJe0gKxF8wytW4MHk11j1VLeTboHsCgiVjRZPw04ieyfiHsaVu8FLIuI2/OyW0TE8jymphcl2wBI\nnQ39mNgPKmoZ1ZV7BdlJ+MXA02TX3txKds3LSItt/g24Iy+/hGyo9MY0Gaqdlz+W7GD/TF7mc2St\no/uale8krnafk2yOtqbfF9mouh+SJbdn8s9yKfDWFuWnkrVonqSuZVjgZ7EJ2cWmf8mfZwKvJEuy\ny4EzgU1bbDsNWDBG3TsA88muy3qOrBX6U7KRgpcBv8x/Vivz9e9oUsdpwLn560nAvNS/5360f3ii\nVLMWJC0GVkfEtqlj6QVJI2QH93Mj4tA+7fPDwNMRcVoP93EvWevtd8Acshkl/rNX+7NquJvObOL6\nWP789T7u821kI+96Ih/Bty1Za3NJPiP4kl7tz6rjZGQ2geTX5LwFeC1Zq+FHEXFDn/a9HfB4jL4w\ntmr7AHdFRC0BXR/FhqtbYk5GZq2Nxz7sXYD/IBvU8H3gQ33cd9Ob6FVsb+puNeFENDx8zsjM+kLS\nJcA7I+KvPaj7VWQzeX+YbGTflRHx/6rej/WOk5GZmSXnGRjMzCw5JyMzM0vOycjMzJJzMjIzs+Sc\njMzMLDknIzMzS87JyMzMknMyMjOz5P4/mDdaHJh1VS4AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b5c18a3d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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ciZI2AYcDKyVdntZ7GtkQVUsl3Zxee2NmZqVQyS7vo+Yu71Za7vJuJTXVu7yb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\nzMwqw0nLzMwqw0nLzMwqw0nLzMwq4/8DfFuX60o8raMAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b5c504050>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Plotting a histogram of the total amplitude within each frequency range also shows nothing \n",
"ampN99 = 'Results/new_data/histograms/amplitudesN99_coarse.npy'\n",
"plot_histogram_from_file(ampN99, larger_system, amplitudes=True,\n",
" ylimits=(-0.1, 0.1), xlimits=(0.01, 0.8))\n",
"plot_histogram_from_file(ampN99, larger_system, amplitudes=True, limited=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Caption\n",
"Histogram of total amplitude ( amplitude = $< FS|f > < f|P_{\\uparrow}| f^{'} > < f^{'}|FS >$ ) against frequency.\n",
"\n",
"Shows no obvious feature near the flutter frequency."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Limiting the transitions we're looking at\n",
"Previously I showed that __different-branch__ transitions cause the flutter.\n",
"\n",
"I now only use those transitions for the graphs I make.\n",
"\n",
"The remaining graphs only account for the __different-branch__ transitions"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b53530e50>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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sAK4FDu6y/+XAKR22hRcvXrx4GXwZNTfUsmfWw7lkCeXd6fGcgjJrgEWSFgLr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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b4cee84d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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S1EJ9MzPrMEW08v3ePZJWA30RsVHSHsD1EbFfVZl5wNKIWJCmPwE8HxGfqShz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b5c3f6e10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Taking intra-branch transitions away from the above histogram shows a noticable peak\n",
"inter_ampN99 = 'Results/new_data/histograms/amplitudesN99_inter_coarse.npy'\n",
"plot_histogram_from_file(inter_ampN99, larger_system, amplitudes=True, ylimits=(-0.0025,0.0025))\n",
"plot_histogram_from_file(inter_ampN99, larger_system, amplitudes=True, ylimits=(-0.0025,0), limited=True)\n",
"\n",
"# Plot the same as above, but on the same scale as we plotted the total amplitude contributions\n",
"plot_histogram_from_file(inter_ampN99, larger_system, amplitudes=True, ylimits=(-0.014, 0), limited=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Caption\n",
"Amplitude histograms, created in exactly the same way as the previous set of graphs, but only accounting for __different-branch__ transitions.\n",
"\n",
"### First graph\n",
"Amplitude histogram, over a large range of frequencies.\n",
"\n",
"Only accounting for __different-branch__ transitions, we see a peak at the flutter frequency.\n",
"\n",
"### Second graph\n",
"Amplitude histogram limited to close to the flutter frequency.\n",
"\n",
"### Third graph\n",
"Amplitude histogram limited to close to the flutter frequency, on same scale as the limited amplitude histogram of all states (last figure of previous set).\n",
"\n",
"Shows how the peak is very small compared to the __same-branch__ transitions we've now removed."
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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KiFYnjTMzswHT7BrPWspN7KZcv3IzkJqZWXc0Szy/K7GtLYAXjiEWMzMbACMm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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b5c5fca90>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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OzMzMBkOpRCTpxaQpfo4C1gGuA/4xIua3MTYzMxsAE11HtB7wUeBY0oSm9wLH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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b5c2519d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Doing similar when showing the number of states doesn't give us anything interesting\n",
"inter_countN99 = 'Results/new_data/histograms/countN99_inter_coarse.npy'\n",
"plot_histogram_from_file(inter_countN99, larger_system)\n",
"plot_histogram_from_file(inter_countN99, larger_system, limited=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Caption\n",
"Histogram of number of transitions against energy.\n",
"\n",
"Is same as previous set of number histograms, but limited to __different-branch__ transitions.\n",
"\n",
"### The peak in the amplitude of contributions near the flutter frequency is not caused by a peak in the number of states there.\n",
"\n",
"It is caused by the large amplitudes of the transitions with this frequency.\n",
"\n",
"This is similar to the way the revival period of the momentum is defined by where transitions have a large amplitude, not by the number of states at the corresponding frequency."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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N+fXbStLs9P1mwP4k992y2rp+bu4rEBHrJB0D/JCkJ9zpEbFS0tHp+tMi4gJJ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\nJykzM6stJykzM6stJykzM6ut/w/3XwypDY66rQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1198684390>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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WrwDeWff6UuDSbuundTNaLL8F2CVfxGZmNmh5jsyuAw5M55vWI2km2fVdV/cTmFmxPCy7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\nzCrPyczMzCrPyczMzCrPyczMzCrv/wMyPk4Tix+I8gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1198684850>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## For a smaller system, this peak isn't so clear\n",
"inter_ampN45 = 'Results/new_data/histograms/ampN45.npy'\n",
"plot_histogram_from_file(inter_ampN45, smaller_system, amplitudes=True, ylimits=(-0.0025,0.0025))\n",
"plot_histogram_from_file(inter_ampN45, smaller_system, amplitudes=True, ylimits=(-0.0025,0), limited=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Caption\n",
"For a smaller system the peak in the amplitude at the flutter frequency is not so clear.\n",
"\n",
"### Parameters:\n",
"N = 45\n",
"\n",
"L=135\n",
"\n",
"m_q=30\n",
"\n",
"V=1.0\n",
"\n",
"$\\gamma = 3$\n",
"\n",
"$Q = \\frac{4}{3} k_F$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Conclusion\n",
"While there is a peak in the amplitudes of the states, which sharpens with increasing system size, it is not caused by a singularity in the number of states, but is caused by the average amplitudes of the states near that frequency.\n",
"\n",
"### Not obvious in fourier transform\n",
"This is not to say that there are transitions of notably large amplitude near this frequency, the fourier transform below doesn't show this."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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F5jrMGnsUc86YjwlVV+6a87GxrjSs1Bws4kceJRO3n2JdhPE+zqfcweMATNBW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\nSMc9+Z8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72ea199250>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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WscsxWCx96lxVaathsTqZ9vbXDn2kXWMdvm16IE+7zw72deZp4spL5yVcrPkK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\n5M5P4GgrKcN+y60AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72e2bb2f50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## These files contain frequencies and amplitudes of different_branch transitions.\n",
"## The transitions are limited in frequency, and only contain those with absolute \n",
"## amplitude above a threshold.\n",
"\n",
"plot_fourier_transform('Results/new_data/inter_amps/N99L297q66V1_00_cache20000.npy',\n",
" larger_system,\n",
" 'N=99',\n",
" (-0.0003, 0.0003))\n",
"plot_fourier_transform('Results/new_data/inter_amps/N45L135q30V1_00_cache20000.npy',\n",
" smaller_system,\n",
" 'N=45',\n",
" (-0.0013, 0.0013))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Caption\n",
"The fourier transform of these __different-branch__ contributions doesn't show any obvious feature at this frequency. \n",
"\n",
"These graphs show the fourier transform of only different-branch transitions.\n",
"i.e. instead of bucketing the amplitudes, we show a scatter graph of all individual transitions.\n",
"\n",
"### First graph -- larger system\n",
"\n",
"### Second graph -- smaller system\n",
"This graph is on a different scale to the larger system, so the shape of both can be seen.\n",
"\n",
"### Difference\n",
"The progression to a clearer peak we see in the histogram of amplitudes is not obvious from the fourier transform.\n",
"\n",
"As the system size increases, the __different-branch__ transitions individually lose amplitude, but the shape stays the same.\n",
"\n",
"The features smoothen out in the fourier transform, which is (probably) why the amplitude histogram peak becomes clearer."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# States responsible\n",
"I believe the main transitions responsible for the __majority__ of this peak in the amplitudes at the flutter frequency are states excited from the negative pseudo edge to another state with the same pseudo particle.\n",
"\n",
"Looking at the contribution from all transitions that are from a state in the negative pseudo edge to a state with a different pseudo _hole_, but the same pseudo _particle_ we get the below.\n",
"\n",
"This is fitting, as the negative pseudo edge states are kinematically disallowed when the initial momentum is below the Fermi momentum, and there's no flutter then."
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import plotting_functions as pf\n",
"import partial_mom as pm\n"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def negative_edge_contributions(cachename, cachelen, ampname):\n",
" \"\"\"Get the contributions that include states from the negative edge\"\"\"\n",
" families, par = pf.get_family_eigenstates(cachename, cachelen)\n",
" edge_val = (par.N - 1) / 2\n",
"\n",
" negative_edge_coords = pm.main_with_others_same_particle(families, -(edge_val + 1))\n",
" negative_edge_amps = pm.get_part_amps(negative_edge_coords, ampname, cachelen)\n",
" negative_edge_amp_array = pm.np_array_from_dict(negative_edge_amps)\n",
" return negative_edge_amp_array, par\n",
"\n",
"\n",
"def normalise_array(transition_array, par):\n",
" \"\"\"Takes an array and normalises it\"\"\"\n",
" transition_array['freq'] = abs(transition_array['freq'])\n",
" transition_array['freq'] /= E_F(par)\n",
" transition_array['amp'] /= k_F(par)\n",
" return transition_array\n",
"\n",
"\n",
"def all_inter_branch():\n",
" \"\"\"Contribution from all transitions between states in different families\"\"\"\n",
" axesdimension = (0.10, 0.10, 0.80, 0.80)\n",
" inter_plotpoints = 'Results/new_data/inter_family_plotpoints.npy'\n",
" momname = 'Results/new_data/mompts/momentum_pointsN99L297q66V1_00_cache20000.npy' # datasets['single']['mompts'][0]\n",
"\n",
" totaldata = np.load(momname)\n",
" inter_data = np.load(inter_plotpoints)\n",
"\n",
" fermi_time = 1. / E_F(par)\n",
" trev = par.L / initial_q(par)\n",
" timelist = pf.maketimepoints(trev, 0, 2, 1000)\n",
" normalised_time = timelist / fermi_time\n",
"\n",
" otherplot_points = pf.form_points(negative_edge_amp_array,\n",
" (k_F(par), initial_q(par)),\n",
" timelist)\n",
" fig = plt.figure()\n",
" ax = fig.add_axes(axesdimension)\n",
" ax2 = ax.twinx()\n",
"\n",
" ax.plot(totaldata['time'], totaldata['momentum'], c='b',\n",
" label='Total Momentum')\n",
" ax2.plot(normalised_time, otherplot_points, c='k',\n",
" label='Same Pseudo Particle, From pseudo hole -50')\n",
" ax2.plot(inter_data['time'], inter_data['momentum'], c='g',\n",
" label='Inter-Branch Contributions')\n",
"\n",
" ax.set_ylabel('Momentum $k/k_{F}$', fontsize=20)\n",
" ax.set_xlabel('Time $t/t_{F}$', fontsize=20)\n",
" ax2.set_ylabel('Momentum $k/k_{F}$', fontsize=20)\n",
"\n",
" ax.set_ylim(0.2, 0.5)\n",
" ax.set_xlim(0, 150)\n",
" ax2.set_ylim(1.25, 1.55)\n",
" ax2.set_xlim(0, 150)\n",
"\n",
" lines, labels = ax.get_legend_handles_labels()\n",
" lines2, labels2 = ax2.get_legend_handles_labels()\n",
"\n",
" plt.legend(lines + lines2, labels + labels2)\n",
" plt.show()\n",
"\n",
" \n",
"def plot_histogram(edges, values, bar_width, yaxislabel):\n",
" plt.bar(edges[:-1], values, width=bar_width)\n",
" plt.xlabel(r'Frequency $\\omega / E_F$', fontsize=20)\n",
" plt.ylabel(yaxislabel, fontsize=20)\n",
" plt.axvline(flutter_frequency,c='r')\n",
" plt.xlim(0, 1)\n",
" return\n",
" \n",
"def plot_fourier(transition_array):\n",
" plt.scatter(transition_array['freq'], transition_array['amp'])\n",
" plt.ylabel(r'Amplitude $k / k_F$', fontsize=20)\n",
" plt.xlabel(r'Frequency $\\omega / E_F$', fontsize=20)\n",
" plt.axvline(flutter_frequency, c='r')\n",
" return"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"cachename = 'Results/new_data/sqlite/N99L297q66V1.00.sqlite'\n",
"cachelen = 20000\n",
"ampname = 'Results/new_data/Ordered_amplitude_matrices/N99L297q66V1_00_cache20000.mem'\n",
"negative_edge_amp_array, par = negative_edge_contributions(cachename, cachelen, ampname)"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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IC2Al4KPJvPW8pOeBLYh/8LKiAbvaHmt7vO0DHCapawkldSLwpKSTJS1EvOEvAPyzqP7L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\nCFENgiAIgjrx/wE6V0kGhy8PHgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72e304f9d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"all_inter_branch()\n",
"negative_edge_amp_array = normalise_array(negative_edge_amp_array, par)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Caption\n",
"The majority of the flutter contribution comes from these transitions to/from the negative edge states (but not all)\n",
"\n",
"Total momentum plotted on left Y axis, others plotted on right Y axis\n",
"\n",
"Scale between the two is just shifted, same magnitude scale"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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6Y/1ytdanKbKNPtHK9EJ5G7inZbdu2ge4OyKWAkj6DmnNjDsaPcnMzMrXbFBe\naWt0t2AL1l1170FSV10zM+uyXiaDZgb+Gp+Z2bDo5ynKfwO8ouLxK0i1i3XUbziqdTmu0SW6vOW9\nrffnb2/b+ls7dd7+et2Dsa3X56/8TqnxSSmw5ECebYOkYQN3L0nagNTAfQjwEPALqhq4zcysO/q2\nZhERqyR9CPgJacrzrzlRmJn1Rt/WLMzMrH/0cwM3QK6BeZL+Jdv/S0l7dDvGbmr2fkj6y+x9uFnS\nFZJe3Ys4Oy3vgE1Je0taJekt3Yyvm3L+jYxJulHSrZLGuxxi1+T4+5gi6YeSbsrei/f2IMyOk3SW\npOWSbmlQptj3ZkT07Y10+eluYA5pTqqbSKPIK8u8Ebgou78vcHWv4+7x+7E/MCW7f9gwvh953oeK\ncpcCFwJH9zruHn4mpgK3AVtmjzfvddw9fC/+HvjcxPsAPA5s0OvYO/BeHAjsAdxSZ3/h781+r1n8\nYWBeRKwEJgbmVToSWAgQEdcAUyXN6G6YXdP0/YiIqyJiRfbwGmDLLsfYDXk+F5AW5ToXeLSbwXVZ\nnvfiL4DvRcSDABHxWJdj7JY878UaYNPs/qbA4xGxqosxdkVE/Jw080Y9hb83+z1Z1BqYt0WOMsP4\nBQn53o9K7wcu6mhEvdH0fZC0BemL4vRs07A2zuX5TGwPTJe0WNJ1kt7dtei6K8978RVgF0kPAb8E\nPtql2PpN4e/Nvu0Nlcn7B15ropdhlPt1SToIOBY4oHPh9Eye9+GLpBmSQ5JoPGBkkOV5LyYDe5K6\noW8MXCXp6oj4VUcj674878VhwA0RcZCkbYFFknaLiN91OLZ+VOh7s9+TRZ6BedVltsy2DaO8AxVf\nDZwJHBYDvXphXXneh72A76Q8webAGyStjIgLuhNi1+R5Lx4AHouI54DnJF0G7AYMW7LI8168lzST\nNhFxj6R7gR2B67oRYB8p/L3Z75ehrgO2lzRH0obA24HqP/YLgPcASNoPeCoilnc3zK5p+n5Img18\nH3hXRNzdgxi7oen7EBHbRMTWEbE1qd3iA0OYKCDf38gPgNdImiRpY1KD5u1djrMb8rwX95Nmsia7\nRr8j8OuuRtkfCn9v9nXNIuoMzJN0fLb/jIi4SNIbJd1Nmkb9fT0MuaPyvB/Ap0gzBJ+e/Ve9MiL2\n6VXMnZDzfRgJOf9G7pT0Y+BmUgPvmRExdMki5+fis8DXJd1Mugzz8Yh4omdBd4ikbwNzgc0lPUBa\n6XQytP4xgb9nAAAIHElEQVS96UF5ZmbWVL9fhjIzsz7gZGFmZk05WZiZWVNOFmZm1pSThZmZNeVk\nYWZmTTlZmJlZU04WZmbWlJOFmTUl6c97HYP1lpOFmTUkaSeyeYRsdPX13FDWe5LWNCnyvohY2JVg\nrFf+Aviv6o3Z1O8/ALYDdiLNMXQlaf4pSPMzzQR2Jc3D9CcRcUM3ArbyeW4oayhLFgF8uk6R8yPi\n5i6GZF0m6XrgTyPihTr75wKLgc9GxMk19r8KuBrYLiIe7miw1jGuWVguEfGZXsdg3SdpH+C2eoki\n89rs509r7YyIWyQtdqIYbG6zsFJkawiskXS2pB0kfVfSI5JWZ/95TpTbV9K5kpZJekHS/ZK+KmlW\ng2N/SNJtkp6T9KCkL0uaImlptnjNRLmxLIb1/rvN9q9TvmpfrriqXuccSd+R9FgW27WS3tTgdeyT\nvS+/kfS8pIck/UTS27L9O2XHvrTBMW6R9PsurjP/l8C3mpSZCzxHqj0AIGkDSZtUlBnWBclGhmsW\nVrZtSV8adwHfBF4MrACQdCzw76QvlgtIK7jtABwHHCFpv4ioXBcYSV8CPgw8BJwBrCKtrb0vaX7+\nWv/xNrq2ut6+VuICtgKuAe4hLXy/GWmxnR9IOjQixqvO8Vek9cBXZuf4FTAD+BPgA8B/Z+tOLAYO\nkrR99bKnkv6UdP3/3G4s8CVpEjAGnNCgzGRgf+DKiFhZsettwKOsrW18v0NhWrdEhG++1b2RGivX\nkBZPWVB1m1dRbk5F2X+ocZwdgN8DS4BZVfsOJiWB71dt/9PseEuAqRXbX8TahtRfV2wfy7Z9qs5r\nWVpZvpW4ql7nJ6vK/1m2/X+qtu9CShKPATvXiOvlFfePzo7xf2uU+3q275Acv7fJwOeblDkduLXB\n/tcBX25yjP2zmD5RsW068Atg415/fn0r79bzAHzr71vFF2Ot26UV5Sa+RB8CJtc4zhey/W+oc57z\nsi/UTSq2nZk9Z16N8nNLShaF4qp4nb8m6yBSVf4+4JGqbV/OnvPRHO/3JNIlm0eBDSu2TwWeBZbk\n/L2dALy6SZmzsrg2r7P/bGD/Jsc4MTvGVcCPSLWtF4Cre/3Z9a3cmy9DWR4REZNylv1lrHs5YsL+\n2c8xSfvW2P8y0hfljsBE98o9SZeNflaj/BWs7aLZjlbiArgpsm/LKg+QLpFV2i/7+aNmwUTEakln\nkpbHPRr4drbr3cBGpMtlDWXrT78iqnqpSZoe6y4h+mHSJb2nahxjI2D3iLiqyenmkpLD3Ij4ffbc\n44Dtm8Vpg8XJwsq2rM72zbKff9fguQFUNopOyX6ud30+0nrLjxUPr5S4oMYXbGYV63ccmZodI28j\n778DnwCOZ22y+F+kL+Wzczz/z4AfV26QdFR2jD80wEfEM5LGI2JVjWO8Cbio0UmyNo0DgOsmEkVm\nBXBZRblXASsi4v4csVufcm8oK1u9xuUV2b5NI+KP6twmRcTPq54DaWDXOiRtAGxetXmiplHvn6Cp\nJcVV1ERi2TJP4Yh4iNQI/lpJO1Y0bJ8XEY/nOMShpMtBlY4Erq/cIGkOcFudY7yD5r2gdgdeAlS/\nN9cBl1Q8/mvA3WYHnJOFdctVpFG8r21WsML12XPm1tj3Gtb//D6Z/ZxdXVjSdsCmJcVV1MQ53lDg\nOf+W/TyeVCOA1BssjzmkRvtKu7L+KOxPk3qsrUPSFGB2RNze5DwT79nllRsj4t6IeD471tbA7yYu\nTUp6iaQFkp6RdKGkT2S3UyTdJWlBjtdnvdDrRhPf+vtG+m99dY5yc7KyZ9XZvyPpMspdwPY19m8I\nHFi1baI31K+AaRXbNyJ9AVc3cG9A+i/+SeClFdtfTLqksk75VuLK8TrHq98vYGfSl/fj1O4NtWWd\nY92ZPecZ4PYCv7MfAm+uePxhYDUpAUBKsp8Bvlbn+ccCH89xnvNJl92mNCjzver3FZiWPW/Xqu17\nAsf1+jPvW+2b2yysKyLirmw8w1nAbZJ+TEoCk0k1gQNJbRO7VDznSklfJn3Z3Srpe6SeSUeRvkQf\nrjrHqmxcxieBGyWdT0ogh5LaCx4i/YffVlw5VJ/jDkkfBL6axfUD4G5Se8nepEthB9c4zleB/5fd\nb9qwXeF6YKGk72evYRfSf/+LJI2TagQvUL829XbSGJO6ssuABwJ3RMSKGvtnAp8jJflfVe0+GFge\nEbdlZV8aEY9mMdUcNGl9oNfZyrf+vlFSzaKi3CtJjbRLgedJYw9uJvX5H6vznL8Bbs/KP0jqirop\nNbrCZuVPJH0Zv5CVOYVUu7i3VvkicTV7naQ5kmq+X6ReUeeSks8L2Wu5CHhLnfJTSTWCZ6ioWeX4\nXUwjDYZ7Ovu5PfBqUhJ8FPgaML3Oc2cC4w2OvSOwiDQuZTWpFvdjUk+vHwGXZr+rldn+Y2oc46vA\nN7P7k4AFvf6c+9b85okEbWBJWgqsiYhteh1LJ0gaI335fjMi5nXpnB8Dno+Ir3bwHHeTaj+3AoeR\nRqR/oVPns3L4MpRZ//p49vMrXTznW0k9pzoi64G1Dam29mA2o+2DnTqflcfJwqyPZGMSDgf2Iv3X\n/cOIuLZL594OeCrWHbhXttcBd0XERIK4JvJ1B7Yec7KwQTaM11D3BP6R1Oh9DvDBLp675iJHJTuU\niqnMnSgGh9sszAwASRcA74iIZztw7N1IM9F+jNQz67KI+Keyz2Od42RhZmZNeQS3mZk15WRhZmZN\nOVmYmVlTThZmZtaUk4WZmTXlZGFmZk05WZiZWVNOFmZm1tT/B2APD1cZs0rxAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72e304ffd0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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Vuwz4L+CgKnynmsVV8ndqDrC4188zyphKPk5TgZuBmWl+6wocp8KYejlObpm1\n1+oGbAAi4uqIeCzN/oysV2RHdUuKa8ygO6x0EtPjudnNgOc6rVtCTGNGfpySjwHfIRudptu6o45r\nTFnHqmi/pX2nWsTUybphxXQYcF5ErASIdSMZlXmcmsU0puPj5GTWXqsbsIt8ALigx7qjiguy7rA/\nUjYO5YdGGZOkAyXdSvaX/ZHd1B1xTFDScZK0Hdl//FNycXRUt6S4xt6X8Z0KYO90qvgCSbt0UXfU\nMY2tK+M4zQamSbo87fuILuqOOibo8jjVsWv+qHXcQ0bZ4MRHAmPXXIbZu6afuADeGBH3SXoRsETS\nbRHx41HEFBHnA+dL2gf4POvfoD5o/cZU1nH6MnBMRIQkse4v1LK/U83igvKO1c+B7SPiCWW9mM8H\ndupzv8OMqazjNBnYDfgj4AXA1ZKu6bDuSGOKiDuBN0U2WEVHx8kts/buBbbPzW9P9hfGepR1rjgN\nOCAiHummbglxERH3pdcHge+RnRIYSUy5GH4M7KDsdomV3dQdUUxlHqfXA+dIuotseLWTJR3QYd0y\n4irtWEXEbyPiifT+QmBy2d+pFjGV+Z26B7gkIp6MiIeBK4HXdFh31DEREavSa2fHqd+LfON9Imu9\n/g/ZRcwpFF/EfAnZhc49u61bUlwvADZP7zcFrgLeNqKYXs66W0J2A+4Z5rHqM6bSjlND+TOBd1fh\nO9UirjK/U9Nz/367Aysq8J1qFlOZx+mVwI/IOma8ALiJ7KkiZR6nZjF1fZx8mrGNiFgr6SjgYtbd\ngH2rpI+k9V8FPgtsBZySnXlhTUTs3qxu2XGRjXv53bRsI+CbEVE4qskQYjoIeJ+kNWQ3pB/cqm6Z\nMVHuceqqbr8x9RsX5R6r9wB/KWkt8ARwSKu6ZcZEiccpIm6TdBFwI1knp9Mi4haAso5Ts5gk7UCX\nx8k3TZuZWe35mpmZmdWek5mZmdWek5mZmdWek5mZmdWek5mZmdWek5mZmdWek5mZmdWek5mZmdWe\nk5mZ1ZKkd5Udg1WHk5mZ1Y6kVwLvKzsOqw6PzWi1I6nx4ZmN3h8Ri0YSjJXlMODsxoXpsTTfB3Yk\nG8T2ceCnrHvg6iSy8RFfRfb4mjdExM9HEbANl8dmtNpJySyAv2tS5PyIuHGEIdmISboO2Dsinm6y\nfl/gcuDvI+K4gvWvBq4Bdoz0SBarN7fMrLYi4nNlx2CjJ2l34OZmiSx5c3r9UdHKiLhJ0uVOZOOH\nr5nZuCWoforvAAAHQ0lEQVRplqTnJJ0paSdJ35b0gKRn01/uY+X2kPQdSfdLelrS3ZJOlbRNi20f\nJelmSU9KWinpRElbSlqRHlw5Vm5OimGD1kFav175hnUdxdXwOWdJOkfSQym2/5b0jhafY/d0XO6V\n9JSkVZIulvSnaf0r07Yva7GNmyQ9I2l6szIDdjjwzTZl9iV7nM81YwskbSRp01yZe4cQm5XELTOb\nCF5O9qN2O3AWsAnwGICkI4Gvkf3wLSZ78u1OwAeBd0raMyLuyW9M0gnAx4BVwFeBtcB8YA+yx8AX\ntRhanc/fYF0vcQEvBX5G9kDERcALyZ7N9n1Jb42IpQ37+BBwCrAm7eNOsodKvgH4S+A/0/OmLgfe\nIml2ZI+zz29jb7LrT9+JiNUtPuNASJoEzAE+0aLMZGAv4KcRsSa36k+BB1nXWvvukMK0MvT7NFFP\nnkY9kV3Mfw44DljYMC3IlZuVK/v5gu3sBDwD3AFs07BuP7Ik9d2G5Xun7d0BTM0tfz7rOhr8Krd8\nTlr22SafZUW+fC9xNXzOzzSUf1ta/sOG5buQJbGHKHiqMLBt7v1BaRv/XFDuG2ndH3Xw7zYZ+FKb\nMqcAv2yxfi5wYptt7JViOja3bBpwLfCCsr+/noYzlR6AJ0/dTrkf7qLpsly5sR/5VcDkgu38a1q/\nf5P9fC/94G+aW3ZaqrOgoPy+A0pmXcWV+5y/InXqaij/v8ADDctOTHX+qoPjPYnslNyDwJTc8qlk\nT1G+o8N/t08Au7Ypc0aKa+sm688E9mqzjaPTNq4GLiRrrT4NXFP2d9fT8CafZrS6ioiY1GHZG2L9\n001j9kqvcyTtUbD+xWQ/5K8Axrpv70Z2WvCKgvJXsa4LeD96iQvgF5F+zRvcQ3YKNG/P9Hphu2Ai\n4llJpwGfJWulfSutOgLYmOx0aEuSpgDbR0MvU0nTIuLXuUUfIztl+2jBNjYGXhsRV7fZ3b5kyWvf\niHgm1f0gMLtdnFZfTmY2EdzfZPkL0+v/a1E3gHyngS3T6wbXhyJiraSHug9vIHFBQQJI1rJhZ6+p\naRuddoL4GnAs8BHWJbMPkyWNMzuo/zbgovwCSfPTNn7fQSUiHpe0NCLWFmzjHcAFrXaSrqm9EVg2\nlsiSx4Arc+VeDTwWEXd3ELvVgHsz2kTQrPPFY2ndFhHxvCbTpIj4cUMdyG68XY+kjYCtGxaPtdSa\n/eE4dUBxdWss8c3spHBErCLrJPJmSa/Idfz4XkQ83MEm3kp2ui/vAOC6/AJJs4Cbm2zjENr3Ynwt\nsDnQeGyWAZfm5v8CcLf8ccTJzCayq8lGgXhzu4I516U6+xasexMb/p96JL2+pLGwpB2BLQYUV7fG\n9rF/F3VOTq8fIWtRQdabsxOzyDq15L2KDUfx+DuyHqfrkbQl8JKIuKXNfsaO2U/yCyPiroh4Km3r\nZcBvx049S9pc0kJJj0v6L0nHpul4SbdLWtjB57OylX3RzpOnbiey1s6zHZSblcqe0WT9K8hOk90O\nzC5YPwXYp2HZWG/GO4Gtcss3JksQjR1ANiJrBT0CvCi3fBOyU2brle8lrg4+59LG4wXsTJZcHqa4\nN+PMJtu6LdV5HLili3+zHwAH5uY/BjxLlqAg+yPgc8DpTeofCfxtB/s5n+y06pYtypzXeFyBrVK9\nVzUs3w34YNnfeU/tJ18zswkrIm5P93OdAdws6SKyJDWZrCW1D9m1sV1ydX4q6USyH+NfSjqPrGfh\nfLIf+fsa9rE23Zf2GeB6SeeTJbi3kl2vWkXWQuorrg407uNWSR8FTk1xfR9YTna97g/JTnXuV7Cd\nU4F/Se/bdvzIuQ5YJOm76TPsQtZ6WiJpKVmL6mmat0YPJrvHrql0mncf4NaIeKxg/QzgC2R/hNzZ\nsHo/YHVE3JzKvigiHkwxFd7UbhVTdjb15KnbiQG1zHLl/oCsE8MK4Cmye69uJLvnaU6TOv8HuCWV\nX0nW1X0LCrrap/JHkyWLp1OZ48laZ3cVle8mrnafk2yMwsLjRdar8TtkyfHp9FkuAN7dpPxUshbV\n4+Raph38W2xFdrPy79LrbGBXsiT9IHA6MK1J3RnA0hbbfgWwhOy+vGfJWsEXkfXUvBC4LP1brUnr\n31uwjVOBs9L7ScDCsr/nnrqbPNCw2QBJWgE8FxE7lB3LMEiaQ5YczoqIBSPa58eBpyLi1CHuYzlZ\n6/GXwDyyEU3+dVj7s8HzaUYz68bfpteTRrjP95D1fByK1INyB7LW7so0Iv/KYe3PhsPJzMxaSvdk\n/QnwerJWyw8i4r9HtO8dgUdj/RurB20ucHtEjCWwn0VntxtYhTiZmQ3WeDxvvxvwD2SdQs4FPjrC\nfRc+hHPA3kruUTFOZPXka2ZmVlmSFgOHRMQTQ9j2a8hG0v84Wc/KKyPiHwe9HxsNJzMzM6s9jwBi\nZma152RmZma152RmZma152RmZma152RmZma152RmZma152RmZma152RmZma19/8B/SAcTCOoNaYA\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72e301c610>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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ZCtrVy7YJ+FS9lX4gbQypFhsX2z/Zkdq95dWuMKIr8ZQsnPeOPkzeWvzeMX7L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\nuLA5juM4DcX/B6Jn1YOy4uC1AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72e1d65150>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Count histogram\n",
"values, edges = np.histogram(negative_edge_amp_array['freq'], bins=np.arange(0, 3, 0.005))\n",
"plot_histogram(edges, values, (0.8*edges[1]), r'Number of Transitions')\n",
"plt.show()\n",
"\n",
"# Amplitude histogram\n",
"values, edges = np.histogram(negative_edge_amp_array['freq'], weights=negative_edge_amp_array['amp'], bins=np.arange(0,3,0.005))\n",
"plot_histogram(edges, values, (0.8*edges[1]), r'Amplitude $k / k_F$')\n",
"plt.xlim(0.2, 0.65)\n",
"plt.ylim(-0.0025, 0)\n",
"plt.show()\n",
"\n",
"# Fourier Transform of momentum contribution (i.e. scatter graph)\n",
"plot_fourier(negative_edge_amp_array)\n",
"plt.ylim(-0.00005, 0.00005)\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Caption\n",
"\n",
"These three graphs show the contribution from transitions to/from the negative edge of the pseudo sea.\n",
"\n",
"The transitions to/from the negative edge of the pseudo sea to states with the same pseudo particle show a clear peak at the flutter frequency in both number of transitions and amplitude of transitions.\n",
"\n",
"This corresponds to a strong peak in the amplitude histogram.\n",
"\n",
"### First plot\n",
"Number of transitions histogram against energy\n",
"\n",
"### Second plot\n",
"Amplitude histogram against energy -- plotted on the same axes as the different-branch plot above\n",
"\n",
"### Third plot\n",
"Amplitude vs Frequency of each transition"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cachename = 'Results/new_data/sqlite/N45L135q30V1.00.sqlite'\n",
"cachelen = 20000\n",
"ampname = 'Results/new_data/Ordered_amplitude_matrices/N45L135q30V1_00_cache20000.mem'\n",
"\n",
"negative_edge_amp_array = normalise_array(*negative_edge_contributions(cachename, cachelen, ampname))"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Eo13WLwAWAUdGxOEd1u8EXAhsFRF3DjVYGxrXLKyQiDhi1DFY/STtBlzbLVFk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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72e2054ed0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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U1/WSfiVpSS91S4ipt/1UdoeOqk9kpxbvAmaSnWr8JbBDQ5k9gE3T67nANd3W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\n52RmZma19/8BKXz8JowPwVMAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72dd101310>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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3F/DzeJ0NS4CVwE5gaacfynAJLtgGPY+UBWFanTjY+31z66zH7Ds9i6pkHJIn\njPotzEatTsGWOF1Oe4Mf5Ly3wOVWreq+3ONnCr25G1jl51X0TPPdYzX3+6y2daSovVmBlp6Rt/Y9\n9FD392wN5aux8Gp717Lhp8BLOv1QhktwwZb3TAqtDzs6mBTNMsqFcVrYJDOnQbMHS+9lyx/o09eT\nLWxRSEzMi6wEc1WVOUKySKWZJ1AHbUYfEIpBsOUJyiIfhpXWHfsrCtEigVlZQPXtCP1Pyi4SrHlW\ntOljX4bXe+hh4P/OGspXY+EzgBfHv7sIJmDJdTrsB+zR6Ycx3IILttxnkuMtpHm/6Fvb5qzhQdHe\nu8RLRaLyfJkFb/H9Fjcgr4kqQcsxfMibheUY0TRDsM0qzGsDxiP1nrScty55SBVhmCcwK13nbaZO\nnmOl417yBJpvpB6OoaWCLVPRQuDoTne4m4ILtsLn0nWWZsXqt6yqMtm4nb9/rTxPvtFCQV0tUEUW\nH53SuGBbZuUzwakWBHs1AVxJIGWvX5JTXiKks4K10jlmLtCGa2ibYPPQvi/HQ/cE8t1pFc2wdpVU\nsScUDNBpbyiDVHEFxiPlRiHFQrgsXUWTeGtYFXm9lXxuVnJz1irBlrVUrWhF6wJtmIaWCTZKhiNT\nM9dVQ6cfynAJLthGRsgXJEVm6emZXEVLyDV5/ifr2b/WWLuHajySm6aGfWXNUkUOFl7dqCEY6aGV\ngi0xCDkwc101dPqhDJfggm3khiKBU7xRPW2ckhV4UwsG87zygjpzyH1o8rvbgDCsdv1kaZsFa1x4\n9VZopWCbEcPozHXV0KKOTgZWxJf4FsKxynnp5gKrgQdJHaFTKT9wQUy/GpiTij+M4G/nQeCyVPyp\n4R+LX8RwWjO/HA+9EfIH8zyDk8SPZbIp/BAbnKbIb2GRmm+Is5Vh/O4W/WjodLs8NPU7tobydbrh\nDXT0UuAj8fN5wCU5aUYBa6OAHQP8EjioUn7g4JhuTMy3FlC8dwdwePx8MzA3fp4HXN6qL8dD74aC\nQTljBJIrrAoEWN7WicT7SdF6WFpFWCD0mvTutmImNdRN2h6GfxhJgm01pfW+acDqnDRHAstS1+cD\n51fKH2dr6ZndMmAWsDdwfyr+ZODq+PlU4IpWfTkeejtkB/vBA3VWFTnBgoagyGNK4uNwupW7+5pu\nxSrO3DoGBJ3FNbahCKVWzayK1i87/b16aF4YSYLtmdRnpa9T8W8FrkldvyMRQEX5gSuAt6fu/TNw\nIkENuSKCSPydAAAgAElEQVQV/2rgO/HzPIJr8XuAfwOmN/PL8TCyQv4MZLdt5cYjtVgjJjO97Mbj\nxGNK3p6upM5yQWcDVpG5Bhk1nTnWqplVcCSdfxSQh94IjY6dVY+tkfRlwq+2ujGz0xrJJ2kFYTaV\nZUGmfJOU17ZsnHLiKuWvle8AN5jZdkmnE1yK/UVeQkkLU5crzWzlEOp1epL08TUQjkfZfTt8fkzp\nOJjlhGN45qXynfXnsGlB6QiVjXfB/DlBu/5pBh+ns7pCG34CXJ7Kc2rqejnxyKE+WNUXjhMaOApo\nkaSjYfJhsS93lT7vHFdT9+tA0oXQP6b82KJ5wJe3Nrsup31Imk04uHpI1HIe27zqSQppSLCZ2TFF\n9yStlzTNzB6XtDfwRE6yRwleUBKmxziAovx5eR6J8dPzyjKzDan4awnrd0V9Wlh0z3EAzOyTkigJ\nqIHz1fpKqTbm5NzZB5Muhp1bYdOiWM6F8MDFhB91KR4w2LgiCD6A/Sk/a6yS0PsS4Yy7eQRlRloA\nrqIk6NKfAc5g8HlmO8eFc/jyBOGG3LPNQp8mnw3Pj4NJ48Lw8lWC8E7KTc6qc7qR+IN/ZXIt6aJG\nC6o2FZzRaGjR1PRS4loYYe0sz3hkNPC/sR1jGWw8Mig/JeORsYT/9v+lZDxyO3AEYZBIG49MS9X5\nFuCnzZxOe/DAoPWp8TZ44/FkK1dNji84vie9fpbspUsf3TJpF0zYlt4LVq6KrKTCLLqXbJQ+x4KV\nZ3/8XLTOV+YJZHnKJ+S2kkHMXqn6Bp/G7qF3QqNjZ8cb3kBHJwPfI2OuD+wD/Fcq3RuBBwjWjRdU\nyx/vXRjTrwbekIpPzP3XkrKCBD4J/CoKxFuJe/2a9eV48MDAHrVJu6IrrpTvyemWvyUgGfTzrB/z\n9sAVnWqQNR5JOxbOO9EgT7DV8znruzFPkLnj4pEU2i7YgD2BdxH0DdfGv+/EnSA37cvxMLJDvsBJ\n70nLc2p8jgVXUydYPCNuV7HVZTDiqGjckXl3KbeQLBCaaaFXNJPL+1wpLi+NHzHT66HRsbOWNbZB\nSHobcDXQn3P7MklnmNm/NVK24zgJk88OvxfnpeLOPtvs6b2AuI52z6JgTAJxbYuw9gVhzel9gldM\ngTMXBWEwNCysfQ1a/4JkDWxgffAuOPuwsB42P64R7g+cSRg6fhc/J/HzCasBRZxOeA7voNRfgPuA\nZz9qOWtyzsilbsEm6RjgBoLbrCXAD4DHCVaMs4G3AzdI2mhmK5rXVMdx0tiAsYkWwIfHASo36IBg\nMXgMwf5knsqFwnyCAOIHg60x6zfCKBJ6JYH3/DgY3QfvT9Xzd1tgt62hHav+vFwIzgfeR2jzZwlC\n7Vpg23Y4azuM2grP5hqaOCOcBqaGPwK2AIcV3P9TYCvwo05PY4dLwFWRHhoI1LmxOX+D90tiSDZs\nX2zB2GRWVFVOjKq83bblertv4rtby342clWd4ze7J/6RGRodOxtRRR4KfMPM7ioQlHdK+gZhk7Tj\nOA1iOeb/VnF2kt4Hl1VLnkuYuf2coN6cRlgSvwxAcO4YeG4M7A5MPlsSletqDVZB1ek4tdKIYNtG\n8LZRid/GdI7jDIF6BvpyQWiT4XKV7zN7b/y8P0FF+Rky63fA4rj5+tpFUv+CIS/KlZG3Ad33nTnN\npxHB9kPgqCppXhXTOY7TRhJBKE15CpgSYpcTlsM/G1PNB16Uk/tAwkzuPODzAH1wKlL/5rCelb9x\nup62lQTv8+PC8NO52aHTwzSg83wZsIGw3X985t4ehA3QG4CXdlo/O1wCvsbmoc2BsvW5tMl9YiK/\nh5Wb50+ysCfuqLK0Bqk0Axunh7TORYucInvovdDo2Jl41qiZ6Dtyf+A1BP8+PwfWA1OBVxK2APwQ\n+HWOEG3IxVa3I8nMTNVTOk7zKLmgssnwOYXZ2DxKLqjOBNgJo0eV1uI+BLyHMLs7EeNbiGWpfKsI\nlom2JXHfVX+7pjwFi6eU1KBLgLOfjtsYHGeARsfORgTbrnorSTCzFzSat5txweZ0kiDgJiwK+8Te\nT8mh8UKCc57PUS5kPkRQRV6NcRviBOBYygVj4wLOBZtTK42OnY2ssf1hA3kcx+kQNrC2lThFXk5J\nQF2dSrk8Xsvg7xIv+X0lW7EvxTzpdbiSoUntAm7D4rBhPKn7HmCLG5E4TaNuwWZm61rQDsdxWkhJ\nuM1fVH6czSOEGdoqUgYmChuln10ALIJVW8J14hmkkoAbvxDGbK9ubDKa8o3ajtM86lZFOvXjqkhn\nuBDUkpMuLl9zewfwDeBiytWDZ20xNvWJyU+HY2XG/zmM6iupNJdSrqJ8ByXhWKyqdFWkUyuNjp0j\ncs3LcUYqQcA889EwS1pImHl9FnhJTLGccNba1cCO6N5q8RSYMAc2LwqzuFVbQv6sivKhWNY0wjlp\nnwfe2wfjF0mTd0n9m4NgzTt4tPmHkTojl4ZmbJL2Az4M/DHh4M0xeenMzNfj8BmbM/wYPHM7meD+\ndSyl/W5nY2xAGNlZVcg/fkH+DC49kzuZoHZMZnFXE07C6UvVcy6wZbvZ5rEt77jTVbTTKnI28F1g\nN2AH4QTqHTlJzcz2r7dBvYgLNmc4Mtha8vOE9baSitA4NVewlZeRCLj3xXQHUBJ0j8XPaeE5Gng3\nYYYHYffQdWa2wTVIThntFGx3EGZq7wFuMLOGzf9HCi7YnOFKaeZ2muB64B8JQuhLwGPR3P96ovur\nBUXGIKU9c8+PAxsDo8eUjE3SQg7C9tenKJ+xbd1i9rvxreij0720U7BtBW40s3lVEzuACzZneBOE\nUv+i8Fv1nwkrC0HohBlb33bYsrC+vWrJTM76gtrxgNTdowiGJS+L1/cAWwqFpjNyaadg+y3wNTM7\nu97KRiou2JzhTvAHeVkffAz4BxJ1pCFEP2bPNPT+lgScxsEuBTXk2Fj+T4DVwMZbzOwNzemJ00u0\n0yryO8DRDeRzHGfYsmlRUDcmP3QT60iA7VFA1Y+ZfdLsd+PNnnsBbFkAO7fA7w2uM7h/C2xc4ELN\naTaNCLYFQL+kL0hqu05c0mRJKyStkXSLpP6CdHMlrZb0oKTzaskv6YKYfrWkOan4RZJ+I+m5TB27\nSfpGzHObpBe3os+O02qCGvDZBfDk9uBD8h0Ey0YIs6w9Lm5UuKXrSISc2YYXmG0c7+pHpxU0au4/\nE7iNoFNYA2zKS2dmrxtS6/LrvhR4yswujQJrkpmdn0kziuAE7/XAo8D/AKeY2f1F+SUdDNwA/Bmw\nL/A9YKaZmaTDgd8AD5rZnql6zgQOMbMzJZ0EvMXMTs5ps6sinaZTMtiAoR4pU15uv4UDSOdFVeT1\nwEeB3+FqQ6edNDx2NnCMwMuBJwl2uxVDM44tyKl/NTA1fp4GrM5JcySwLHV9PnB+pfzABcB5qTzL\ngFmZcp/LXC8DjoifRwNPFrTZWvEsPIzcQAuPfglH01yfOrZmlsGL499+A5Z3uv8eRkZodOxsRBW5\nGJgMfBx4MTDWzF6QFxoouxammtn6+Dk5LifLvsDDqetHYlyl/PvEdHl5ihiox8x2AJskTa6lE44z\nNCafHY6amRfD5ZRmb0Nl06KSOhKCuf4zBDP9lwF9c4aqlnScVtKId/8jgf8ws4ub3ZgESSsIs6ks\nC9IXZmaS8nSp2TjlxFXKX1ROw0hamLpcaWYrm1W24zQTM/tk8Nb/2T44ldKG7asJQu5cQAsAXx9z\nmkp0ADJ7qOU0Iti2U3IZ0BLM7Jiie5LWS5pmZo9L2pvg+STLo8B+qevpMQ6gKH+lPEU8CrwIeEzS\naGCimW0o6NPCKmU5Th1sWBw89SfMB55t4tEvo7YSNqARrCMfAzYTNlofAPzKfTs6TSf+4F+ZXEu6\nqJFyGlEXfh84vJHKmsRSSj8h5wE35aS5E5gpaYakscBJMV+l/EuBkyWNlbQ/MBO4o462vBW4tc6+\nOE5D2IAV49lPh1DsFaQxNiyOJ2wTrCPfD/wfQfkBMFqSljevPsdpHo1s0H4JwSJyMXCJ1VvAEIlr\nWDcSZkrrgLeZ2UZJ+wDXmNmbY7o3EpzfjQKuNbNPVcof710InEbwfXmWmS2P8ZcCpwB7A7+N9XxC\n0m7AV4BDgaeBky3nvDq3inS6Eal/czi25oQYsz8lt1tQzc2W4wyVdnoe+TIwg7BJ+yHglxSb+59W\nb4N6ERdsTjci7bHZ2NwXzP0hrK3tRfi9GHxJwir38ei0jHYKtpqdHrfQMrKrcMHmdCOlGVsyRiwh\nuNv6HcFi0l1iOa2l0bGzEeORWs9Y86O5HaerSQxIllOaoa0HziAcJPrpmG7+HEkXukrSGS405Hmk\naqHB88dfmtm3m154F+IzNqcbkXShwSKxF6UjZs4iLDWfT/p4G1dJOq2gnU6QKzVihqSLCe6nvtXM\nsh3HaS+lGdhnKW0Ev4ywQ2YV4eDQ5Iw16/NN285wYcgztrh/6zjgdIJvxkS6rnC9e8BnbE7XIpk4\nh/LTrm8iqCR3xw8LdVpJ24xHUhW+hHAW/KnAH8ToJ4EvEszr/6+hgnsQF2xO1yKZmEBw2QXBxH/r\nTthjFHyOcnXkrywcT+M4zaEtqkhJYyS9TdL3CF79PwL0U1I7ftvMPu5CzXF6ifcRfBEsjZ/3eEFw\nk5pVR+6SqyOd4UBNgk3SgZI+Q3Ah9XXgdcDPgQ8Ce5vZW1vXRMdxOssSgveRY+Pn7cAbCL4jd6TS\nvYBwWrbjdJZazf1Xx7+PE9wOXG9m97amSY7jDC8S45GE+TvgyjFh+Nid4G4L4jpbX7tb5zhZ6tnH\nZsB3gW+6UHOckUZ6L9vO7dA3Gl6gwULvwx1pneOkqXWN7WMEE/53Az+VdL+k86J3fMdxeprkbLbE\nGfKovqCOzPtd7H4ZnM5Ts1WkJAFzCKvHxxLe6p3ACoLi/WvAP5vZ6a1pavfiVpFO1yKZmLgF3ttX\nbvJ/zXZ4fgzsRrnF5LPuXstpGm0195c0lTB7ey/lLrbuBM40szvrLrSHccHmtItglZicpL1h8ZDd\nXEkmxm+BcX3ZPWuw+cew+zEwLr7bz7hQc5pK2/exxUpFsJA8HTgeGEPQRawizN6ubLjwHsIFm9MO\nglCbsCgzgxrasTIDM7bL+kpraUuAs7aYbfTN2E5L6YhLLQvcamYnEU6c/giwFvgjgu8dx3HaxuSz\ng1BL3F9dTmn2NhRGba0tznGGB41498/FzJ4k6Co+K2k2QU3pOE7Xs+EumD+ndD0fePaujjXHcarQ\nEu/+TjmuinTaQetUkZOfhndPKTce+fLTZk/vNcQmO05F2nkem+M4wxAz+2RY9j47qh+fHbrxCAA7\nx8ErKBmPLBl6kY7TQrrOYamkyZJWSFoj6RZJ/QXp5kpaLelBSefVkl/SBTH9aklzUvGLJP1G0nOZ\nOk6V9KSkX8RwWiv67Di1YmafNHt6rxCadfDn9r5gCbkkhvnAhsXNKdtxmk/XqSIlXQo8ZWaXRoE1\nyczOz6QZBTxAOEbnUeB/gFPM7P6i/JIOBm4A/ozg4fV7wEwzM0mHEzaoP2hme6bqmQccZmbzq7TZ\nVZFOdyKZuB4/VNTpBMPioNE2kXhiJf49PifN4cBaM1tnZtsJjpuPq5L/OOBrZrbdzNYRrDuPADCz\nO8zs8Zx6ROn8OcfpYd4AfJPgecRXMJzhTTe+oVPNbH38vB6YmpNmX+Dh1PUjRCFVIf8+wG2ZPPtW\naYsBJ0o6mjBD/LCZPVJTLxynazg383lHUULHGRYMS8EmaQVB95Gl7EiMqCbM06Vm45QTVyl/UTlZ\nvgPcYGbbJZ1OmAH+RZU8jtNlzCOcxZZ8/rLvYXOGNcNSsJnZMUX3JK2XNM3MHo9OmJ/ISfYosF/q\nenqMAyjKXylPUTs3pC6vBS6t0O6FqcuVZrayUtmOM3y4hswWAt/D5rSEuAd69pDL6VLjkafN7NOS\nzgf6c4xHRhNUg39BWO2+g3LjkUH5U8Yjh1MyHjnAUg9I0nMZ45FpydqbpLcA/8/MXpXTZjcecboT\nycQ5+B42pxOMJOORS4BjJK0h+Km8BEDSPpL+C8DMdgAfIBwidR/wDTO7v1J+M7sPuDGm/y7BmbPF\nsi+V9DAwTtLDkj4ey5ov6VeSfhnrO7W1XXec+pB0oTTlqRB0YWOlvIJgOPLN+NlxhjddN2PrRnzG\n5nSCoXoikXShwSKxF6XN2U3wZuI4NdIR7/5ObbhgczqBNOUpWDyl3Cv/2TWrEaUpTxkbpohl+B42\npxOMJFWk4zhtYee48Nf3sDndhb+ljtOzbFgM8xeVrucDz9bhCivZr5b4M/A9bE534KrINuCqSKdT\nDOVEbal/s7GpT5wQY9wi0mkv7t3fcZxBREFWt6FHEIh9feHq2Bhb74zPcTqDr7E5zgiidvP/iQvg\nC/HzUuBqYOcWt4Z0ugEXbI4zQiiZ/y+eEsKERXnCLcSprxSTGI7s5q60nK7A19jagK+xOcOBWs3/\npf7N8N4++CrGesKxNb5/zWk/bu7vOM6QKc3WXkHJGtLVkE534YLNcUYMGxaHmdcSgun+h4Cd48rV\nkRMXwHuA84DkCML7gM2LcJwuwVWRbcBVkc5wIQix8QtgVF/W1RZwNPTPgc+TnJhtfAsx3r2NOB3B\nXWoNY1ywOcOJwWtt5wJfNBitMFv7KvBpAIxTEfjamtMRfB+b4zgNsJygmjwkDh7J2lriG3JgL5zj\ndA2+xuY4I470WttCguf+fYCjKK2tHUtYW3Oc7sNVkW3AVZHOcKPkassmw+cU1tTmAe8AfgKsBjbe\nYjAHf3edDuFrbMMYF2zOcKX8zLZVwLWAbYFNi8zsk0jmgs3pFC7YhjEu2JzhTEVHyS7YnA7igm0Y\n44LN6VpcsDkdxD2POI7jOA5dKNgkTZa0QtIaSbdI6i9IN1fSakkPSjqvlvySLojpV0uaE+PGSfov\nSfdL+pWkT6XS7ybpGzHPbZJe3Mq+O47jONXpOsEGnA+sMLMDgVvjdRmSRgFXAnOBg4FTJB1UKb+k\ng4GTYvq5wBckJVPgS83sIOBQ4ChJc2P8e4CnzWwm8DmSXa0jDEmzO92GVuL96256uX+93Leh0I2C\n7VhK3lmXAMfnpDkcWGtm68xsO/B14Lgq+Y8DvmZm281sHbAWOMLMtprZDwBiWT8H9s0p65vAXwy9\ne13J7E43oMXM7nQDWszsTjegxczudANayOxON2A40o2CbaqZrY+f1wNTc9LsCzycun6EkjAqyr9P\nTJeXB4CotvwrwkyvrB4z2wFskjS53g45juM4zWNYutSStIKwYzTLgvSFmZmkPLPObJxy4irlH1SO\npNHA14DL4ozOcRzHGYYMS8FmZscU3ZO0XtI0M3tc0t7AEznJHgX2S11Pj3EARfkr5YHgPO8BM7s8\nFfco8CLgsSj4JprZhoJ29/S+CkkXdboNrWRE968H3t1e/v56uW+NMiwFWxWWEnz/fDr+vSknzZ3A\nTEkzCJ5cTwJOqZJ/KXCDpMUEFeNM4A4ASRcDEwjGInltuQ14KyUVZRm+h81xHKd9dN0G7biGdSNh\nprQOeJuZbZS0D3CNmb05pnsj4WCpUcC1ZvapSvnjvQuB04AdwFlmtlzSdOA3wP3AttiMK8zsOkm7\nAV8hWEs+DZzsakrHcZzO0nWCzXEcx3Eq0Y1WkcOeWjaRS9pP0vcl3Rs3fs/vRFvroWjTeybN5fH+\n3ZIObXcbh0K1/kl6e+zXPZJ+IumPOtHORqjlu4vp/kzSDkkntLN9Q6XGd3O2pF/E/7eVbW7ikKjh\n3Zwo6TuSfhn7d2oHmtkQkq6LthOrKqSpb1wxMw9NDsClwEfi5/OAS3LSTAP+JH7eA3gAOKjTba/Q\np1GEvX0zgDHAL7PtBd4E3Bw/HwHc1ul2N7l/RxIMhCBs4u+K/tXSt1S6/wb+Ezix0+1u8nfXD9wL\nTI/Xe3W63U3u34XAp5K+EZZGRne67TX279WE5ZxVBffrHld8xtYaqm4iN7PHzeyX8fPvCGt4+7St\nhfVTadN7wkC/zex2oF9S3j7D4UjV/pnZz8xsU7y8nWA52w3U8t0BfBD4d+DJdjauCdTSv78Bvmlm\njwCY2VNtbuNQqKV/uwgGbsS/T1vYWzvsMbMfAc9USFL3uOKCrTXUsol8gGi9eShhsByuVNr0XilN\ntwz+tfQvzXuAm1vaouZRtW+S9iUMllfFqG5afK/lu5sJTI7q/zslvbNtrRs6tfTvSuBgSY8BdwNn\ntalt7aDucaUbzf2HBU3YRJ6UswfhV/JZceY2XKl1oMtubeiWAbLmdkp6LcF69qjWNaep1NK3zwPn\nx/dVDP4ehzO19G8M8EqC27s+4GeSbjOzB1vasuZQS//mAj83s9dKegmwQtIfm9lzLW5bu6hrXHHB\n1iA29E3kSBpD8DH5VTPL2483nMhuYN+PchdkeWmym9yHM7X0j2gwcg0w18wqqU+GE7X07TDg69Hv\n917AGyVtN7Ol7WnikKilfw8DT5nZVmCrpB8Cfwx0g2CrpX+nAp8CMLP/lfQQ8FLCnt5up+5xxVWR\nrSHZuA0Fm8jjr+JrgfvM7PNtbFujDGx6lzSWsOk9O+gtBd4FIGkWsDGlkh3uVO2fpBcB3wLeYWZr\nO9DGRqnaNzP7QzPb38z2J2gQ/rZLhBrU9m5+G/hzSaMk9RGMEO5rczsbpZb+/QZ4PUBcf3op8Ou2\ntrJ11D2u+IytNVwC3CjpPcRN4ACZTeRHAe8A7pH0i5jvAjNb1oH2VsXMdkj6ALCc0qb3+yWdEe9/\n0cxulvQmSWuBzcC7O9jkuqilf8DHgUnAVXFms93MDu9Um2ulxr51LTW+m6slLQPuIRhaXGNmXSHY\navz+/gG4XtI9BLXdR6zAvd9wQ9LXgKOBvSQ9DFxEUB03PK74Bm3HcRynp3BVpOM4jtNTuGBzHMdx\negoXbI7jOE5P4YLNcRzH6SlcsDmO4zg9hQs2x3Ecp6dwweY4juP0FC7YHMdxnJ7CBZvjOD2FpLd0\nug1OZ3HB5jhOzyDpZUS/gs7IxX1FOj2DpF1VkrzbzJZUSeN0N38D3JCNjE7Hvw0cALyM4HPwpwS/\nkRB8ME4DXk7wtfinZvbzdjTYaT7uK9LpGaJgM+DvC5LcZGb3tLFJTpuRdBfwKjN7vuD+0cD3gX8w\ns4ty7r8CuA04wMx+29LGOi3DZ2xOz2Fmn+h0G5z2I+lw4N4ioRZ5Tfz7vbybZrZK0vddqHU3vsbm\njDjiuVa7JH1Z0oGSviHpCUk74y/6JN0Rkv5d0uOSnpf0G0lXx8Nji8r+gKR7JW2V9IikKyRNlLQu\nHv6YpJsd2zBo1hDvl6XP3KupXZl+zpD0dUlPxbb9j6Q3V+jH4fG5PCrp95Iek7Rc0l/H+y+LZf93\nhTJWSdoWzwdrB28H/rVKmqOBrYRZGQCSRksan0rTLYfjOgX4jM0ZybyEMMA9AHwFGAdsApB0GvAl\nwiC4lHAC84HAe4G/kjTLzB5OFybpMuCDwGPAF4EdwHGEQy3HAHkziUprAYPuNdIu4MXA7cD/AkuA\nKYTDKr8t6fVmtjJTx/uAq4DtsY4HganAnwJ/C/xbPN/s+8BrJc00swczZbyKsF717+04bFbSKGA2\n8OEKacYARwI/NbPtqVt/DTxJaRb3rRY102kXZubBQ08EgiHALsJBhQszYV4q3YxU2otzyjkQ2Aas\nAfbO3HsdQWB9KxP/qljeGqA/Fb8bJSOFX6fiZ8e4jxf0ZV06fSPtyvTzY5n0c2L8f2XiDyYItKeA\ng3LatU/q84mxjM/kpLs+3vuLGr63McA/VklzFfCrCvePAa6oUsaRsU0LUnGTgTuAvk6/vx6aFzre\nAA8emhVSg3he+O9UumTAfwwYk1PO5+L9NxbU8x9x8B+firsm5pmXk/7oJgm2utqV6ueviYZimfT/\nBzyRibsi5jmrhuc9iqC2exIYm4rvB7YAa2r83j4M/FGVNNfFdu1VcP/LwJFVyjgvlvEz4LuEWezz\nwG2dfnc9NDe4KtLpNczMRtWY9m4rV0klHBn/zpZ0RM79PyAM6i8FEpPwVxJUhz/ISf8TSmblQ6GR\ndgH80uLInuFhgpo0zaz497vVGmNmOyVdA3ycMHv7Wrz1TmB3gsq0IpLGAvtZxlpV0mQz25CK+iBB\nrbsxp4zdgT8xs59Vqe5ogiA72sy2xbzvBWZWa6fTXbhgc0YyjxfET4l//1+FvAakDQ4mxr+D1pPM\nbIekp+pvXlPaBTnCILKDwQZk/bGMWg0ovgQsAM6gJNhOJwiQL9eQfw6wLB0h6bhYxoBxi5ltlrTS\nzHbklPFm4OZKlcQ1uKOAOxOhFtkE/DCV7hXAJjP7TQ1td4YpbhXpjGSKDDc2xXsTzOwFBWGUmf0o\nkwfCJt8yJI0G9spEJzO4oh+X/U1qV70kQnB6LYnN7DGCgclrJL00ZTTyH2b2dA1FvJ6gEkxzLHBX\nOkLSDODegjJOpro15J8AewLZZ3MncGvq+v2Am/p3OS7YHGcwPyN4n3hNtYQp7op5js659+cM/l97\nJv59UTaxpAOACU1qV70kdbyxjjxfiH/PIMy0IFiF1sIMgkFMmpcz2HvI3xMsV8uQNBF4kZndV6We\n5Jn9OB1pZg+Z2e9jWfsDzyXqaUl7SlooabOk/5S0IIZLJD0gaWEN/XM6QacX+Tx4aFYgzIJ21pBu\nRkx7XcH9lxJUaQ8AM3PujwVenYlLrCIfBCal4ncnCIus8chowuzoGeCFqfhxBLVaWfpG2lVDP1dm\nnxdwEEHQPE2+VeT0grJWxzybgfvq+M6+Axyfuv4gsJMgrCD8IPgEcG1B/tOAj9RQz00E1evECmm+\nmX2uwKSY7+WZ+FcC7+30O+8hP/gam+NkMLMH4n6x64B7JS0jCKwxhBnWqwlraQen8vxU0hWEgflX\nkr5JsFA8jjDg/zZTx4647+1jwC8k3UQQdq8nrG89Rpg5DaldNZCt435JZwJXx3Z9G1hLWN/7M4I6\n9HYXoSsAAAIKSURBVHU55VwNLI6fqxqNpLgLWCLpW7EPBxNmVSskrSTMtJ6neJZ6EmEPXyFRFfxq\n4H4z25RzfxrwKcIPkgczt18HrDeze2PaF5rZk7FNuRvonWFApyWrBw/NCjRpxpZKdwjBAGId8HvC\n3q57CHuqZhfk+Tvgvpj+EYL5/ARyzPdj+vMIguP5mOYSwqztobz09bSrWj8JPhNznxfBOvLfCYLy\n+diXm4ETCtL3E2Zam0nNWGv4LiYRNkb/Lv6dCfwRQWA/CVwLTC7IOw1YWaHslwIrCPv+dhJmx8sI\nFp/fBf47flfb4/235ZRxNfCV+HkUsLDT77mH6sGdIDtOG5C0DthlZn/Y6ba0AkmzCYLiK2Y2r011\nfgj4vZld3cI61hJmlb8C5hI8qXyuVfU5zcFVkY7jNIOPxL9XtrHOtxIsKFtCtMT8Q8Is+JF4csAj\nrarPaR4u2BzHaYi45+svgcMIs5nvmNn/tKnuA4CNVr6Ju9kcAzxgZokwu91q28LgdBgXbI7THnpR\n5/9KYBHBoORG4Mw21p17oGiTeT2p421cqHUPvsbmOE7XIWkpcLKZbWlB2X9M8Pj/IYKF5g/N7JPN\nrsdpHS7YHMdxnJ7CPY84juM4PYULNsdxHKencMHmOI7j9BQu2BzHcZyewgWb4ziO01O4YHMcx3F6\nChdsjuM4Tk/hgs1xHMfpKf4/+X2H8RSRhjAAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f72e1edb110>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"values, edges = np.histogram(negative_edge_amp_array['freq'], bins=np.arange(0, 3, 0.005))\n",
"plot_histogram(edges, values, (0.8*edges[1]), r'Number of Transitions')\n",
"plt.show()\n",
"\n",
"values, edges = np.histogram(negative_edge_amp_array['freq'], weights=negative_edge_amp_array['amp'], bins=np.arange(0,3,0.005))\n",
"plot_histogram(edges, values, (0.8*edges[1]), r'Amplitude $k / k_F$')\n",
"plt.xlim(0.2, 0.65)\n",
"plt.ylim(-0.0025, 0)\n",
"plt.show()\n",
"\n",
"plot_fourier(negative_edge_amp_array)\n",
"plt.ylim(-0.0002, 0.0002)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Caption\n",
"\n",
"## Same as above, but for the smaller system\n",
"\n",
"Is less smooth"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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