Moyal and tomographic probability representations for f-oscillator quantum states
Vladimir I. Man’ko, Giuseppe Marmo, F. Zaccaria
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 the Moyal equation for the quantum f-oscillator, which provide solutions for the partial case of f-nonlinearity existing in Kerr media. Nonlinear coherent states and the thermodynamics of nonlinear oscillators are studied.
arXiv:0912.3424•Physica Scripta•Mar 12, 2010•12 citations