Semiclassical propagation of Wigner functions

Journal Article · Mon Jun 07 04:00:00 EDT 2010 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3425881· OSTI ID:21559859

Dittrich, T; Gomez, E A; Pachon, L A ^[1]; CeiBA-Complejidad, Bogota D.C. ^[2]

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1. Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia)
2. Colombia

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schroedinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

• OSTI ID: 21559859
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 21 Vol. 132; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AIRY FUNCTIONS
ALGORITHMS
ANNIHILATION OPERATORS
APPROXIMATIONS
BENCHMARKS
CALCULATION METHODS
CHAOS THEORY
DIFFERENTIAL EQUATIONS
EIGENSTATES
ELECTRONIC EQUIPMENT
EQUATIONS
EQUIPMENT
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONS
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
MONTE CARLO METHOD
OPTICS
OSCILLATORS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
PROPAGATOR
QUANTUM OPERATORS
SCHROEDINGER EQUATION
SEMICLASSICAL APPROXIMATION
SPACE
TUNNEL EFFECT
WAVE EQUATIONS