Moyal and tomographic probability representations for f-oscillator quantum states

DOI10.1088/0031-8949/81/04/045004zbMATH Open1189.81052arXiv0912.3424OpenAlexW1973893742MaRDI QIDQ3563656

F. Zaccaria, Vladimir I. Man'ko, Giuseppe Marmo

Publication date: 1 June 2010

Published in: Physica Scripta (Search for Journal in Brave)

Abstract: States of nonlinear quantum oscillators (f-oscillators) are considered in the Weyl-Wigner-Moyal representation and the tomographic probability representation, where the states are described by standard probability distributions instead of wave functions or density matrices. The evolving integrals of motion for classical and quantum f-oscillators are found and the solution for the Liouville equation associated with the probability distribution on the phase space for this oscillator is obtained along with the solution of Moyal equation for quantum f-oscillator, which provide the solutions for partial case of f-nonlinearity existing in Kerr media. Nonlinear coherent states and the thermodynamics of nonlinear oscillators are studied.

Full work available at URL: https://arxiv.org/abs/0912.3424

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Quantum state estimation, approximate cloning (81P50)