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Published on: May 30, 2014
Semiclassical propagation of Wigner functions.
T Dittrich1, E A Gómez, L A Pachón
1Departamento de Física, Universidad Nacional de Colombia, Bogotá DC, Colombia. tdittrich@unal.edu.co
The Journal of Chemical Physics
|June 10, 2010
Summary
This study explores semiclassical phase-space propagation using Wigner representation, offering accurate numerical methods for quantum dynamics. The approach effectively handles complex quantum effects and classical chaos in molecular systems.
Area of Science:
- Quantum mechanics
- Computational chemistry
- Physical chemistry
Background:
- Semiclassical methods are crucial for understanding quantum dynamics in complex systems.
- The Wigner representation offers a phase-space perspective on quantum mechanics.
Purpose of the Study:
- To investigate semiclassical phase-space propagation in the Wigner representation for numerical applications.
- To evaluate two distinct semiclassical approximation schemes for quantum dynamics.
Main Methods:
- Utilizing van Vleck's approximation for the Wigner function propagator.
- Employing phase-space path integration with Airy functions to resolve quantum caustics.
- Applying methods to nonlinear molecular potentials (Morse oscillator, quartic double well).
Main Results:
- Semiclassical Wigner propagation demonstrates high accuracy even with significant quantum effects like tunneling and Schrödinger cat states.
- The methods successfully capture classical chaos in multidimensional phase spaces.
- Autocorrelation functions and coherent state propagation were accurately computed.
Conclusions:
- Semiclassical Wigner propagation is a robust method for quantum dynamics, applicable to challenging systems.
- The study provides effective numerical implementation strategies, including Monte-Carlo-Metropolis integration for high-dimensional problems.
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