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

TL;DR

This paper investigates how small deviations from Boltzmann-Gibbs statistics in Tsallis framework affect the $x^{4}$ quantum model, revealing temperature-dependent modulation of quantum squeezing.

Contribution

It provides a perturbative analysis of the $x^{4}$ model under Tsallis statistics, highlighting the impact of environmental deviations on quantum squeezing angles.

Findings

Deviations from BG statistics significantly affect the squeeze angle at high temperatures.

The squeeze angle exhibits a dip structure as a function of inverse temperature.

The sign of the squeeze angle changes with temperature, indicating frequency modulation.

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.