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Moving Boundary Truncated Grid Method: Application to the Time Evolution of Distribution Functions in Phase Space.
Tsung-Yen Lee1, Chun-Yaung Lu2, Chia-Chun Chou1
1Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan.
The Journal of Physical Chemistry. A
|December 29, 2020
Summary
The moving boundary truncated grid (TG) method efficiently simulates phase space distribution functions, accurately capturing negative basins and reducing computational cost for quantum dynamics.
Area of Science:
- Computational Physics
- Quantum Mechanics
- Numerical Methods
Background:
- The time-dependent Schrödinger equation governs quantum systems.
- Simulating distribution functions in phase space is computationally intensive.
- Existing methods struggle with negative probability basins.
Purpose of the Study:
- Extend the truncated grid (TG) method for phase space distribution function evolution.
- Develop an adaptive method for accurate and efficient simulations.
- Investigate the TG method's ability to capture negative basins.
Main Methods:
- Adaptive determination of phase space grid boundaries.
- Variable activation/deactivation of grid points.
- Integration of Klein-Kramers, Wigner-Moyal, and modified Caldeira-Leggett equations.
Main Results:
- The TG method accurately propagates distribution functions, including negative basins.
- Significant reduction in computational effort compared to full grid methods.
- No prior knowledge of phase space dynamics is required.
Conclusions:
- The extended TG method offers an efficient and accurate approach for phase space simulations.
- It overcomes limitations of trajectory-based methods in capturing interference effects.
- The TG method is a valuable tool for quantum dynamics and statistical physics problems.
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