ollama run gemma:text pulling manifest pulling df18cdedaff1... 100% ▕█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▏ 5.2 GB pulling 097a36493f71... 100% ▕█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▏ 8.4 KB pulling 4b98b1f4c59c... 100% ▕█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▏ 21 B pulling 11a9f1a6054c... 100% ▕█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▏ 409 B verifying sha256 digest writing manifest removing any unused layers success
ur a Fokker-Planck, laddie !:) The problem is, however, that in the real world the "initial condition" is not a Dirac delta function but rather a Gaussian whose standard deviation is not small compared to the width of the potential well. In other words, the quantum walker is not a wave packet localized near the minimum of the potential, but rather a wave packet that is initially extended over the whole width of the well. As a result, the quantum walker will not follow the path dictated by the stationary phase approximation, but rather a more complex trajectory, which is the subject of the next section.
The other problem with the stationary phase approximation is that it only describes the trajectory of the wave packet, not its width. In other words, the stationary phase approximation describes the "average" trajectory, but does not take into account the fluctuations of the width of the wave packet. These fluctuations are important because they lead to the decoherence of the quantum walker, as we shall see.
The decoherence of the quantum walker is also different from the decoherence that occurs in the "real" world, where the wave packet width is initially small and only grows over time. In other words, the decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of a wave packet in the real world is a "temporal" phenomenon. This distinction is important because it means that the decoherence of the quantum walker is a much faster process than the decoherence of a wave packet in the real world.
The decoherence of the quantum walker is a "real-time" phenomenon, whereas the decoherence of