Thermodynamics of Pseudo-Hermitian Systems in Equilibrium

Abstract

In study of pseudo(quasi)-hermitian operators, the key role is played by the positive-definite metric operator. It enables physical interpretation of the considered systems. In the article, we study the pseudo-hermitian systems with constant number of particles in equilibrium. We show that the explicit knowledge of the metric operator is not essential for study of thermodynamic properties of the system. We introduce a simple example where the physically relevant quantities are derived without explicit calculation of either metric operator or spectrum of the Hamiltonian.

9 pages, 2 figures, to appear in Mod.Phys.Lett. A; historical part of sec. 2.1 reformulated, references corrected; typos corrected

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• Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator
• Non-Hermitian Chiral Magnetic Effect in Equilibrium
• Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
• Phase transitions and thermodynamic cycles in the broken PT-regime
• Features, paradoxes and amendments of perturbative non-Hermitian quantum mechanics
• Coulomb potential and the paradoxes of PT-symmetrization
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics