Casimir eigenmode summation

main.rs

use std::f32::consts::PI;

/// The exponent coefficient. Determines the contribution from higher frequencies.
const S: f32 = 0.01;

/// The discrete distance difference to use.
const DELTA_D: f32 = 0.01;

/// The total size of the box, after which the geometry is periodic.
const TOTAL_DISTANCE: f32 = 1.0;

/// After the contribution from a frequency is lower than this value, the computation will stop.
const MIN_CONTRIBUTION: f32 = 1e-10;

fn main() {
    let start = DELTA_D * 5.0;
    let end = TOTAL_DISTANCE * 0.1;
    let step = 0.001;
    let mut d = start;
    println!("distance force");
    while d < end {
        println!("{} {}", d, casimir_force(d));
        d += step;
    }
}

fn casimir_force(distance: f32) -> f32 {
    (total_casimir_energy(distance + DELTA_D / 2.0) - total_casimir_energy(distance - DELTA_D / 2.0)) / DELTA_D
}

fn total_casimir_energy(distance: f32) -> f32 {
    partial_casimir_energy(distance) + partial_casimir_energy(TOTAL_DISTANCE - distance)
}

fn partial_casimir_energy(distance: f32) -> f32 {
    let mut energy = 0.0;
    for n in 1.. {
        let omega = PI * n as f32 / distance;
        let contribution = omega * (-S * omega).exp();
        energy += contribution;
        if contribution < MIN_CONTRIBUTION {
            break;
        }
    }
    0.5 * energy
}