Wigner phase space distribution via classical adiabatic switching

Journal Article · Mon Sep 21 00:00:00 EDT 2015 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4930271· OSTI ID:22489598

Bose, Amartya ^[1]; Makri, Nancy ^[1]

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1. Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States)

Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.

• OSTI ID: 22489598
• Journal Information: Journal of Chemical Physics, Vol. 143, Issue 11; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
DEGREES OF FREEDOM
DENSITY
DISTRIBUTION
DISTURBANCES
EIGENSTATES
EVALUATION
HAMILTONIANS
HARMONIC OSCILLATORS
PERTURBATION THEORY
PHASE SPACE
QUANTUM MECHANICS
TEMPERATURE RANGE
THERMODYNAMIC PROPERTIES
TIME DEPENDENCE
WIGNER DISTRIBUTION
WKB APPROXIMATION