Dynamics of coherent states and the Husimi time evolution operator

Gang Ren, Jian-ming Du, Hai-jun Yu +1 more

Liyun Hu

On the basis of the technique of integration within an ordered product of operators and the coherent state representation,we investigate the evolution of Husimi function of excitation on coherent state in a dissipative channel.For the first time we derive the analytical expression for Husimi function and then discuss the effect of some parameters on this Husimi function.

Prakash Chand

Go. Torres-Vega, John H. Frederick

We present a time evolution equation that provides a novel basis for the treatment of quantum systems in phase space and for the investigation of the quantum-classical correspondence. Through the use of a generalized Husimi transform, we obtain a phase space representation of the time-dependent Schrödinger equation directly from the coordinate representation. Such an equation governs the time evolution of densities such as the Husimi density entirely in phase space, without recourse to a coordinate or momentum representation. As an application of the phase-space Schrödinger equation, we compute the eigenfunctions of the harmonic oscillator in phase space, relate these to the Husimi transform of coordinate representation eigenstates, and investigate the coherent state, its time evolution, and classical limit (ℏ→0) for the probability density generated by this state. Finally, we discuss our results as they relate to the quantum-classical correspondence, and quasiclassical trajectory simulations of quantum dynamics.

C. L. Mehta, E. C. G. Sudarshan

R. Román-Ancheyta, Manuel Berrondo, J. Récamier

We study the temporal evolution of a coherent state under the action of a parametric oscillator and a nonlinear Kerr-like medium. We make use of the interaction-picture representation and use an exact time-evolution operator for the time-independent part of the Hamiltonian. We approximate the interaction-picture Hamiltonian in such a way as to make it a member of a Lie algebra. The corresponding time-evolution operator behaves like a squeezing operator due to the temporal dependence of the oscillator’s frequency. We analyze the probability amplitude, the auto-correlation function, and the Husimi distribution function for different Hamiltonian parameters. We find very good agreement between our approximate results and converged numerical calculations.