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Simulation of the time evolution of the Wigner function with a first-principles Monte Carlo method
M S Torres1, G Tosi, J M A Figueiredo
1Departamento de Fisica, Universidade Federal de Minas Gerais, PO Box 702, Belo Horizonte, MG, Brazil. marzojr@fisica.ufmg.br
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
This study introduces a novel Monte Carlo method using hidden variables to overcome quantum phase-space limitations. It enables classical computation of full quantum time evolution for arbitrary states and potentials.
Area of Science:
- Quantum mechanics
- Computational physics
- Statistical mechanics
Background:
- Monte Carlo methods are powerful computational tools.
- Quantum phase-space information is challenging to access directly.
- Quasiprobability densities limit direct application of classical methods in quantum mechanics.
Purpose of the Study:
- To develop a first-principles Monte Carlo method for quantum systems.
- To overcome limitations imposed by quasiprobability densities.
- To enable classical computation of quantum time evolution.
Main Methods:
- Employed a hidden variables representation within a Monte Carlo framework.
- Developed a classical Monte Carlo algorithm for quantum time evolution.
- Addressed systems with time-dependent potentials.
Main Results:
- Successfully calculated the full quantum time evolution of arbitrary initial quantum states.
- Demonstrated a viable classical approach to quantum dynamics.
- Provided guidelines for practical algorithm implementation.
Conclusions:
- The hidden variables Monte Carlo method effectively bypasses quasiprobability density limitations.
- This approach facilitates accurate quantum simulations on classical hardware.
- The method is applicable to complex, time-varying quantum systems.
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