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

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 $\beta_p$ and the coupling strength $\lambda_p$. 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 $\beta_p$ has a dip structure, and the dip is deeper with the increase of $\lambda_p$. The angle as a function of $\beta_p$ changes the sign. These facts indicate that the frequency is modulated by the difference between these statistics.