Evolution of the coherent state via a new time evolution operator

Michael Kollmann

Prakash Chand

M. A. Rego-Monteiro, Evaldo M. F. Curado, Ligia M. C. S. Rodrigues

We analyze the time evolution of two kinds of coherent states for a particle in a P\"oschl-Teller potential. We find a pair of canonically conjugate operators and compare the behavior of their time evolution for both coherent states. The nonlinear ones are more localized. The trajectory in the phase space of the mean values of these two operators is a kind of generalization of the Rose algebraic curves. The new pair of canonically conjugate variables leads to a fourth-order Schr\"odinger equation which has the same energy spectrum as the P\"oschl-Teller system.

Xiang‐Guo Meng, Ji‐Suo Wang, Bao‐Long Liang

Using thermal entangled state representation, we solve the master equation of a diffusive anharmonic oscillator (AHO) to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation. We present a new evolution formula of the Wigner function (WF) for any initial state of the diffusive AHO by converting the WF calculation into an overlap between two pure states in an enlarged Fock space. It is found that this formula is very convenient in investigating the WF's evolution of any known initial state. As applications, this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of diffusive AHOs.

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

Luis Lorenzo Sánchez-Soto, Eusebio Bernabéu