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

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