Moyal and tomographic probability representations for f-oscillator quantum states

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.

19 pages, submitted to Physica Scripta

References in corpus (8)

• Multiphoton Quantum Optics and Quantum State Engineering
• An introduction to the tomographic picture of quantum mechanics
• Star products, duality and double Lie algebras
• Duality symmetry for star products
• On the meaning and interpretation of Tomography in abstract Hilbert spaces
• Coherent States and Bayesian Duality
• A New Look at the Quantum Mechanics of the Harmonic Oscillator
• Gauge Theory of the Star Product

Cited by in corpus (3)

• Entanglement dynamics and position-momentum entropic uncertainty relation of a $\Lambda$-type three-level atom interacting with a two-mode cavity field in the presence of nonlinearities
• Quantum Kerr oscillators' evolution in phase space: Wigner current, symmetries, shear suppression and special states
• Quantum phase transition of two-level atoms interacting with a finite radiation field