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- Title
Application of optimization method to the x<sup>4</sup> model in the Tsallis nonextensive statistics.
- Authors
Ishihara, Masamichi
- Abstract
We study the effects of the environment described by the Tsallis nonextensive statistics on physical quantities using an optimization method in the case of small deviation from the Boltzmann-Gibbs statistics. The x4 model is used and the density operator is restricted to be a Gaussian form. The variational parameter is the frequency Ω of a harmonic oscillator in the optimization method. We obtain an approximate expression of free energy and of the expectation value of βmΩ2 x2/2, where β is the inverse of the temperature T and m is the mass. The optimized frequency is estimated numerically. The expectation value of βmΩ2 x2/2 and the derivative of the energy with respect to the temperature are also calculated numerically. The effects of the Tsallis nonextensive statistic in the case of small deviation from the Boltzmann-Gibbs statistics are found: (1) the frequency modulation, (2) the variation of the expectation value of βm Ω2 x2/2 and (3) the variation of .
- Subjects
PROCESS optimization; ENVIRONMENTAL impact analysis; BOLTZMANN-Gibbs distribution (Statistical physics); GAUSSIAN beams; APPROXIMATION theory
- Publication
International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics, 2015, Vol 29, Issue 1, p-1
- ISSN
0217-9792
- Publication type
Article
- DOI
10.1142/S0217979214502348