Quantum Behavior of a Nonextensive Oscillatory Dissipative System in the Coherent State

Abstract

We investigate the nonextensivity of a generalized dissipative oscillatory system in the Glauber coherent state. We introduce a parameter q as a measure of the nonextensivity of the system. Considering the characteristic of nonextensivity, the system is described by a deformed Caldirola–Kanai oscillator, which is represented in terms of q. We manage the system by describing the associated Hamiltonian in terms of the harmonic oscillator ladder operators. The time evolutions of the canonical variables, the Hamiltonian expectation value, the quantum energy, and the symmetry-breaking in the evolution of the system, are analyzed in detail regarding their dependence on q, damping factor, and the external driving force. The amplitude of the oscillator is slightly quenched as q becomes large, whereas the amplitude of the canonical momentum is enhanced in response to the growth in q. As q increases, the dissipation of the quantum energy becomes a little faster as a manifestation of the nonextensivity of the system. Our results are compared to the classical results, as well as to those in the previous research performed on the basis of the SU(1,1) coherent states. The coherent states, including the Glauber coherent states, can be convenient resources for carrying information, which is crucial in quantum information processing.

Analysis of the effects of nonextensivity for a generalized dissipative system in the SU(1,1) coherent states

“…Özeren has analyzed the nonextensive properties of a damped oscillator 1 which is described in terms of a deformed exponential function considering the parametric time evolution of the SU(1,1) coherent states. Glauber coherent states for the deformed damped oscillator driven by an external force has also been studied 13 . For several physical systems, the deviation of the decay of energy or signal from the usual exponential falloff was investigated so far 14 – 18 .…”