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arXiv · 1011.0283

Environmental effects on the $x^{4}$ model in Tsallis statistics

Masamichi Ishihara
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Abstract

The author studied the effects of the environment described by Tsallis statistics in quantum mechanics, when the deviation from Boltzmann-Gibbs (BG) statistics is small. The $x^{4}$ model was used and the squeeze angle caused by the difference between Tsallis and BG statistics was calculated perturbatively in the mean field approximation as a function of the dimensionless parameters: the inverse temperature $β_p$ and the coupling strength $λ_p$. The author found that the effect of the deviation from BG statistics is relatively large at high temperature. The squeeze angle as a function of $β_p$ has a dip structure, and the dip is deeper with the increase of $λ_p$. The angle as a function of $β_p$ changes the sign. These facts indicate that the frequency is modulated by the difference between these statistics.

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Masamichi Ishihara. 2010-11-15. Environmental effects on the $x^{4}$ model in Tsallis statistics. https://doi.org/10.1016/j.physa.2011.07.047

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