Linear Response Theory for Non-Hermitian Systems in a Many-Body Context

Non-Hermitian physics can arise in both open and interacting quantum systems. Within pseudo-Hermitian quantum mechanics, the inner product on the Hilbert space of a non-Hermitian Hamiltonian is furnished with a positive-definite metric. By using their respective Green's functions, we examine the dynamics of non-Hermitian systems and characterize the distinctions between pseudo-Hermitian quantum mechanics and standard interacting theory. We determine the implications of the use of the pseudo-metric operator in pseudo-Hermitian quantum mechanics on the Green's functions and the associated linear-response formulae. Furthermore, within the context of conditional dynamics, we develop a finite-temperature and many-body extension to the previously developed zero-temperature non-Hermitian Kubo formula. Using these Kubo formulae, we contrast the longitudinal conductivity of a Dirac-like model for various non-Hermitian formalisms.