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- W3099775066 abstract "The Tsallis q-exponential function $e_{q}(x) = (1+(1-q)x)^{frac {1}{1-q}}$ is found to be associated with the deformed oscillator defined by the relations $left [N,a^{dagger }right ] = a^{dagger }$ , [N,a] = −a, and $left [a,a^{dagger }right ] = phi _{T}(N+1)-phi _{T}(N)$ , 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→2 it becomes a two-level system with a nondegenerate ground state and an infinitely degenerate excited state." @default.
- W3099775066 created "2020-11-23" @default.
- W3099775066 creator A5081421761 @default.
- W3099775066 creator A5084820991 @default.
- W3099775066 date "2020-07-04" @default.
- W3099775066 modified "2023-10-17" @default.
- W3099775066 title "On the Deformed Oscillator and the Deformed Derivative Associated with the Tsallis q-exponential" @default.
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- W3099775066 doi "https://doi.org/10.1007/s10773-020-04534-w" @default.
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