A study of the x4 model in the Tsallis nonextensive statistics

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 x4 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 βp and the coupling strength λp. 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 βp has a dip structure, and the dip is deeper with the increase of λp. The sign of the angle as a function of βp changes. These facts indicate that the frequency is modulated by the difference between these statistics.