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Open AccessArticle

Deforming Gibbs Factor Using Tsallis q-Exponential with a Complex Parameter: An Ideal Bose Gas Case

Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov St., UA-79005 Lviv, Ukraine
Symmetry 2020, 12(5), 732; https://doi.org/10.3390/sym12050732
Received: 29 March 2020 / Revised: 15 April 2020 / Accepted: 28 April 2020 / Published: 5 May 2020
(This article belongs to the Special Issue PT-Symmetry in Physical Systems)
The paper presents a study of a non-standard model of fractional statistics. The exponential of the Gibbs factor in the expression for the occupation numbers of ideal bosons is substituted with the Tsallis q-exponential and the parameter q = 1 α is considered complex. Such an approach predicts quantum critical phenomena, which might be associated with PT -symmetry breaking. Thermodynamic functions are calculated for this system. Analysis is made both numerically and analytically. Singularities in the temperature dependence of fugacity and specific heat are revealed. The critical temperature is defined by non-analyticities in the expressions for the occupation numbers. Due to essentially transcendental nature of the respective equations, only numerical estimations are reported for several values of parameters. In the limit of α 0 some simplifications are obtained in equations defining the temperature dependence of fugacity and relations defining the critical temperature. Applications of the proposed model are expected in physical problems with energy dissipation and inderdisciplinarily in effective description of complex systems to describe phenomena with non-monotonic dependencies. View Full-Text
Keywords: deformed statistics; fractional statistics; Tsallis q-exponential; ideal Bose gas; complex statistics parameter; critical temperature; fugacity; specific heat deformed statistics; fractional statistics; Tsallis q-exponential; ideal Bose gas; complex statistics parameter; critical temperature; fugacity; specific heat
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Rovenchak, A. Deforming Gibbs Factor Using Tsallis q-Exponential with a Complex Parameter: An Ideal Bose Gas Case. Symmetry 2020, 12, 732.

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