Rotating Morse wave packet dynamics of diatomic molecule

Roy, Utpal; Ghosh, Suranjana

doi:10.48550/arxiv.0907.3116

Cited by 1 publication

(1 citation statement)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We choose the Morse oscillator for a detailed study of semiclassical Wigner propagation for two reasons: Above all, being prototypical for strongly anharmonic molecular potentials and correspondingly complex dynamics [67][68][69][70], it is a widely used benchmark for numerical methods in this realm [4,21,[71][72][73]. Secondly, the Morse oscillator has the remarkable advantage, shared only with very few other potentials, that closed analytical expressions are available not only for its energy eigenstates [74] but even for their Wigner representations [71], a feature that greatly facilitates the comparison with exact quantum-mechanical results [43,71,[75][76][77][78] and hence provides a solid basis for an objective test of the performance of semiclassical approximations to the propagator.…”

Section: Morse Oscillatormentioning

confidence: 99%

Semiclassical propagation of Wigner functions

Dittrich,

Gomez,

Pachon

2009

Preprint

View full text Add to dashboard Cite

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 Schrödinger 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.

show abstract