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Physics Letters A

Semiclassical analysis of the eigenstate Wigner functions for the discrete self-trapping equation

Sergio De Filippo, M. Fusco Girard, Mario Salerno

Published Jun 1, 1990• 0 citations
Publisher
DOI
10.1016/0375-9601(90)90961-m

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In this work we study the Wigner functions, which are the quantum analogues of the classical phase space density, and show how a full rigorous semiclassical scheme for all orders of ℏ can be constructed for them without referring to the actual coordinate space wavefunctions from which the Wigner functions are typically calculated. We find such a picture by a careful analysis around the stationary points of the main quantization equation, and apply this approach to the harmonic oscillator solving it for all orders of ℏ.
The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wigner function is written for some chosen states associated to discrete angle and angular momentum variables, and the time evolution is numerically calculated using the discrete von Neumann-Liouville equation. Direct evidences in the time evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU (2)-based semiclassical continuous approach to the Lipkin model is also presented.