Quantum Dynamics in a Bistable System

NOTE: This is a longer version of one of my previous videos. I had to speed it up a bit, so that you wouldn't be waiting for minutes for something to happen. The program took 45 min to run! The notes are below:

This is a Quantum Tunneling simulation in Mathematica that solves the time-dependent schroedinger equation.

Here, a gaussian wavepacket is placed in a potential system that has two stable states (bistable). This simulation was created as a quantum extension of the classic stochastic resonance phenomenon, where a particle oscillates between the two stable states. Here, however, the probability density function (pdf) of the particle's postion is not a delta function (and thus could have a finite density in both wells simultaneously). However, in this case, the pdf seems to pass through one and a half period of oscillation between two wells, and it is possible that a longer simulation will enable us to analyze the dynamics more clearly. However, this is still not a recreation of stochastic resonance - which needs a periodic and a random fluctuation of the potential. This work is currently in progress.

This plot shows the progression of the probability density of the single-dimensional wavepacket in time.


Created by Biswaroop Mukherjee under the guidance of Dr. Antonio Nassar as a part of a Studies in Scientific Research project in Harvard-Westlake School, North Hollywood, CA.

Category:

Nonprofits & Activism

Tags:

• Quantum
• simulation
• mathematica
• schroedinger
• bistable
• stochastic
• resonance
• physics
• math
• graphing
• science
• technology

[polzowatel]

this is very precise indeed