Abstract
The characteristics of nonextensivity for a general quantum dissipative oscillatory system in the SU(1,1) coherent states are investigated using the invariant operator method. We consider a deformed Caldirola-Kanai oscillator represented in terms of a parameter q which is a measure of the degree of nonextensivity. The nonextensivity effects on the parametric evolution of the SU(1,1) coherent states are elucidated. We compare our results with those of previous researches and address the advantage of our methodology which adopts the linear invariant operator. In particular, the nonextensive behaviors associated with the fluctuations of canonical variables and the dissipation of quantum energy are analyzed in detail regarding their dependence on q. The properties of SU(1,1) coherent states that we adopt here can be utilized in quantum-information processes such as cloning, swapping, and teleportation of state information.
Highlights
As is well known, Boltzmann-Gibbs (BG) statistics achieved remarkable success, because it provides a standard way of thermostatistical analyses incorporated with ergodic theory
Özeren has analyzed the nonextensive properties of a damped o scillator1 which is described in terms of a deformed exponential function considering the parametric time evolution of the SU[1,1] coherent states
Inspired by the above-mentioned usefulness of the Lewis-Riesenfeld invariant formalism in the context of time-dependent systems, we investigate in this work the nonextensive dynamics of the SU[1,1] coherent states for the generalized damped harmonic oscillator using a linear invariant operator
Summary
Boltzmann-Gibbs (BG) statistics achieved remarkable success, because it provides a standard way of thermostatistical analyses incorporated with ergodic theory. It has turned out that the statistical behavior of some dynamical systems and associated phenomena does not follow BG statistics They include long-range spatial and/or temporal interactions, long-range microscopic memory, and dissipative m ultifractals. Tsallis introduced a generalized thermostatistics with a concept of nonextensive entropy in Ref. 4, which is suitable for describing the mechanism of nonextensivity Soon after this seminal report, it turned out that Tsallis statistics is very useful in the analyses of overall nonextensive dynamical phenomena, including black-body radiation5, gravitation, Euler turbulence, biological e volution, intrinsic inhomogeneities in m anganites, nonlinear dynamical d issipation, etc.. Inspired by the above-mentioned usefulness of the Lewis-Riesenfeld invariant formalism in the context of time-dependent systems, we investigate in this work the nonextensive dynamics of the SU[1,1] coherent states for the generalized damped harmonic oscillator using a linear invariant operator. The advantage of the use of DCOIOT in the research of time-dependent harmonic oscillators, such as normal/generalized Caldirola-Kanai (CK) o scillators, is that it enables us to obtain exact quantum solutions (without any approximation) so far as the classical solution of the given system is k nown
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