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.

A typo in the author's name field is corrected. 9 pages, 4 figures

References in corpus (5)

• Power laws in elementary and heavy-ion collisions - A story of fluctuations and nonextensivity?
• Nonextensive hydrodynamics for relativistic heavy-ion collisions
• Modified Hagedorn formula including temperature fluctuation - Estimation of temperatures at RHIC experiments -
• On superstatistical multiplicative-noise processes
• Quantum Field Theories in Nonextensive Tsallis Statistics

Cited by in corpus (2)

• Effects of the Tsallis distribution in the linear sigma model
• Application of optimization method to the $x^4$ model in the Tsallis nonextensive statistics