Quantum-Kicked-Rotor

Python tool which visualizes the quantum kicked rotor in phase space, meaning in the Husimi representation.

Examples

For those two examples I have chosen K=2.5, m=100 and kicks=51.

Example: Chaotic motion

Example: Integrable motion

Features

• Starts animation for the time evolution of the quantum kicked rotor via mouse klick in the plot. The mouse position will be chosen as the initial center of the initial wave packet (maximally located Gaussian)
• If requested, compares the quantum time evolution to the trajectory of the classical kicked rotor.
• If requested, saves every image in the time evolution as *.png and creates a *.mp4 out of it.

Usage

Required packages

This program works with external packages, which are the following:

• numpy

python3 -m pip install numpy

• matplotlib

python3 -m pip install matplotlib

• tqdm (optional, only if progressbar=True)

python3 -m pip install tqdm

FFmpeg

FFmpeg is only needed, if you want to save the animation.

• For Windows simply visit the official ffmpeg website, download and install it. Make sure that ffmpeg is callable in the console via

ffmpeg

• For Ubuntu

sudo apt-get install ffmpeg

Changeable variables

• K : float - Kick strength.

• m : int - Number of planck cells in one direction.

• kicks : int - Number of kicks.

• x0 : float - Initial position of the classical kicked rotor. Together with p0 and a kick strength of K=4.7 this initial condition lead to a integrable island in the phase space.

• p0 : float - Initial momentum of the classical kicked rotor. Together with x0 and a kick strength of K=4.7 this initial condition lead to a integrable island in the phase space.

• saveAni : bool - If "True" every animation step will be saved as *.png in the directory of this python file (total of "kicks" images). After closing the plotting-window those images will be combined into a mp4 video using ffmpeg.

• showClassic : bool - If "True" the animation will show the phase space distribution of the classical kicked rotor. If "False" these points will not be shown.

• progressbar : bool - If "True" the package "tqdm" will be imported. This results in a progressbar while the animation is calculated.

• Default values:

K = 2.5
m = 100
kicks = 11
x0 = 2.31                                       # coordinates of integrable
p0 = 4.47                                       # island for K=4.7
saveAni = True
showClassic = False
progressbar = False