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Gibbs states defined by biorthogonal sequences
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Gibbs states defined by biorthogonal sequences
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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.
Forward citations
Cited by 2 Pith papers
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Kubo-Martin-Schwinger conditions for non-Hermitian systems
Positivity of the biorthogonal Gibbs functional characterizes quasi-Hermiticity for diagonalisable non-Hermitian operators with real spectra, and the resulting state satisfies the three analytic KMS conditions.
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Kubo-Martin-Schwinger conditions for non-Hermitian systems
For any diagonalisable non-Hermitian H with real spectrum, the biorthogonal Gibbs functional satisfies positivity of ω_bi(A†A) for all A if and only if H is quasi-Hermitian.
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