Abstract
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.
Highlights
The concept of space-time reflection symmetry commonly referred to as PT -symmetry [1] has recently entered a vast class of problems in classical and quantum physics, with both theoretical and experimental domains ranging from acoustics and mostly optics to topological insulators and metamaterials, see [2] and references therein
Numerical Results and High-Temperature Behavior In Figures 1 and 2, the results of numerical calculations for fugacity and specific heat are shown for several values of α and s
This is done by analogy with both ordinary ideal Bose gas and its nonadditive generalization [25], where the fugacity equals unity below the critical temperature
Summary
The concept of space-time reflection symmetry commonly referred to as PT -symmetry (parity–time symmetry) [1] has recently entered a vast class of problems in classical and quantum physics, with both theoretical and experimental domains ranging from acoustics and mostly optics to topological insulators and metamaterials, see [2] and references therein. Hamiltonians containing complex-valued potentials [3,4,5,6], PT -symmetry breaking in non-conservative quantum systems is linked to quantum critical phenomena of a special sort [7]. Applications of complex thermodynamic quantities are exemplified by temperature [10], chemical potential [11,12,13], energy [14] or magnetic field [15] Another concept considered in the present work is nonextensive and nonadditive distributions, which originated from information theory almost sixty years ago [16,17].
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