Moyal and tomographic probability representations for f-oscillator quantum states

TL;DR

This paper explores the phase space and tomographic probability representations of nonlinear quantum oscillators, deriving solutions for their dynamics and thermodynamics, and highlighting their applications in Kerr media.

Contribution

It introduces a novel approach to describe f-oscillator states using probability distributions, providing solutions for their classical and quantum evolution.

Findings

Derived integrals of motion for classical and quantum f-oscillators.

Obtained solutions to the Liouville and Moyal equations for f-oscillators.

Studied nonlinear coherent states and thermodynamics of nonlinear oscillators.

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.