Gibbs states defined by biorthogonal sequences
Fabio Bagarello, Camillo Trapani, Salvatore Triolo
TL;DR
This paper explores generalized Gibbs states and KMS-like conditions within PT-quantum mechanics, introducing extended Heisenberg algebra dynamics to analyze properties of related operators.
Contribution
It introduces new connections between similar Hamiltonian operators and extends the Heisenberg algebraic dynamics for PT-quantum systems.
Findings
Generalized Gibbs states satisfy KMS-like conditions
Extended algebraic dynamics reveal new properties of PT-quantum operators
Connections between similar Hamiltonians facilitate analysis of non-Hermitian systems
Abstract
Motivated by the growing interest on PT-quantum mechanics, in this paper we discuss some facts on generalized Gibbs states and on their related KMS-like conditions. To achieve this, we first consider some useful connections between similar (Hamiltonian) operators and we propose some extended version of the Heisenberg algebraic dynamics, deducing some of their properties, useful for our purposes.
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