Spectral and entropic characterizations of Wigner functions: Applications to model vibrational systems
- STC 'Institute for Single Crystals', National Academy of Sciences, Kharkov 61001 (Ukraine)
The Wigner function for the pure quantum states is used as an integral kernel of the non-Hermitian operator K, to which the standard singular value decomposition (SVD) is applied. It provides a set of the squared singular values treated as probabilities of the individual phase-space processes, the latter being described by eigenfunctions of KK{sup +} (for coordinate variables) and K{sup +}K (for momentum variables). Such a SVD representation is employed to obviate the well-known difficulties in the definition of the phase-space entropy measures in terms of the Wigner function that usually allows negative values. In particular, the new measures of nonclassicality are constructed in the form that automatically satisfies additivity for systems composed of noninteracting parts. Furthermore, the emphasis is given on the geometrical interpretation of the full entropy measure as the effective phase-space volume in the Wigner picture of quantum mechanics. The approach is exemplified by considering some generic vibrational systems. Specifically, for eigenstates of the harmonic oscillator and a superposition of coherent states, the singular value spectrum is evaluated analytically. Numerical computations are given for the nonlinear problems (the Morse and double well oscillators, and the Henon-Heiles system). We also discuss the difficulties in implementation of a similar technique for electronic problems.
- OSTI ID:
- 21106223
- Journal Information:
- Journal of Chemical Physics, Vol. 129, Issue 9; Other Information: DOI: 10.1063/1.2968607; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
ANNIHILATION OPERATORS
CALCULATION METHODS
DECOMPOSITION
EIGENFUNCTIONS
EIGENSTATES
ENTROPY
HARMONIC OSCILLATORS
HERMITIAN OPERATORS
KERNELS
NONLINEAR PROBLEMS
OSCILLATORS
PHASE SPACE
POTASSIUM IONS
QUANTUM MECHANICS
VIBRATIONAL STATES
WIGNER DISTRIBUTION