2019/11/30 by Ramaswamy Jagannathan, Sameen Ahmed Khan · 1 citation
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #math.MP #math.QA #quant-ph
paper · pdf · doi:10.1007/s10773-020-04534-w
published as Int. J. Theor. Phys. 59 (2020) 2647-2669 · Third version in which three more references have been added. To appear in International Journal of Theoretical Physics
arxiv created 2020/07/04 · arxiv updated 2020/08/26
The Tsallis q-exponential function eq(x) = (1+(1-q)x)(1)/(1-q) is found to be associated with the deformed oscillator defined by the relations [N,a^†] = a^†, [N,a] = -a, and [a,a^†] = ϕT(N+1)-ϕT(N), with ϕT(N) = N/(1+(q-1)(N-1)). In a Bargmann-like representation of this deformed oscillator the annihilation operator a corresponds to a deformed derivative with the Tsallis q-exponential functions as its eigenfunctions, and the Tsallis q-exponential functions become the coherent states of the deformed oscillator. When q = 2 these deformed oscillator coherent states correspond to states known variously as phase coherent states, harmonious states, or pseudothermal states. Further, when q = 1 this deformed oscillator is a canonical boson oscillator, when 1 < q < 2 its ground state energy is same as for a boson and the excited energy levels lie in a band of finite width, and when q \longrightarrow 2 it becomes a two-level system with a nondegenerate ground state and an infinitely degenerate excited state.