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Pseudo-Hermitian Quantum Mechanics with Unbounded Metric Operators
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We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space, observables, and equivalent Hermitian Hamiltonian for the case that H has a real and discrete spectrum and its eigenvectors belong to the domain of eta and consequently its positive square root.
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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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