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A variational principle in Wigner phase-space with applications to statistical mechanics
1Department of Chemistry, Physical Chemistry, University of Gothenburg, SE-412-96 Gothenburg, Sweden. jens72@chem.gu.se
The Journal of Chemical Physics
|January 26, 2011
Summary
The Dirac-Frenkel variational principle optimizes Wigner distribution time-evolution. This method efficiently cools classical distributions to quantum ones and studies quantum dynamics, offering a systematic approach for many-body systems.
Area of Science:
- Quantum Mechanics
- Computational Physics
- Statistical Mechanics
Background:
- The Wigner distribution function is a key tool for analyzing quantum systems in phase space.
- Simulating quantum dynamics and deriving low-temperature distributions from classical ones presents significant computational challenges.
Purpose of the Study:
- To apply the Dirac-Frenkel variational principle to the Wigner-Liouville equation for both imaginary and real time dynamics.
- To develop a computationally tractable method for studying quantum effects in low-temperature many-body systems.
Main Methods:
- Utilized the Dirac-Frenkel variational principle to determine optimal time-evolution of parameter-dependent Wigner distributions.
- Formulated the variational principle as a principle of least action.
- Incorporated Feynman's path integral centroid variable and employed Metropolis Monte Carlo sampling for local centroid constrained distributions.
Main Results:
- Demonstrated the variational principle's ability to 'cool' high-temperature classical distributions to low-temperature quantum Wigner distributions in imaginary time.
- Analyzed the real-time coherent dynamics of a particle in a double-well potential.
- Showcased the combination of variational methods and Monte Carlo sampling for studying quantum many-body systems.
Conclusions:
- The Dirac-Frenkel variational principle provides an effective framework for Wigner phase-space dynamics.
- The proposed hybrid variational-Monte Carlo method offers a systematically improvable pathway for investigating quantum effects in complex systems.
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