Quantum entropy of systems described by non-Hermitian Hamiltonians

Abstract

We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non-Hermitian case and find that one needs both the normalized and non-normalized density operators in order to properly describe irreversible processes. It turns out that such a generalization monitors the onset of disorder in quantum dissipative systems. We give arguments for why one can consider the generalized entropy as the informational entropy describing the flow of information between the system and the bath. We illustrate the theory by explicitly studying few simple models, including tunneling systems with two energy levels and non-Hermitian detuning.

A comparative study on different non-Hermitian approaches for modeling open quantum systems

“…Dot-dashed red line is the fidelity numerically-obtained steady state based on the NHQM method (see Eqs. (6), (7) and (11) and the Lindblad master equation approach (see Eq.…”

Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides

“…Furthermore, the main difference of the proposed approach from the standard non-Hermitian quantumstatistical one [35][36][37][38][39][40][41] is that the role of the time variable is played here by the third coordinate, z/c. In other words, instead of time evolution of quantum states the method will describe the distribution of EM wave energy along the propagation axis.…”

“…Expanding the discussions presented in Refs. 36,37,40 , let us consider the following "shift" transformation of the decay operator…”

“…Therefore, MS map must be used to develop the corresponding generalization, which is going to be the main goal of this paper . Although the density-operator approach for quantum systems driven by NH Hamiltonians has been long since known (see, for instance, the monograph 35 ), it has been further developed in the works [36][37][38][39][40][41] . In the current paper we adapt this formalism for the purposes of describing the EM wave propagation inside dielectric materials and waveguides in presence of dissipative effects induced by environment, as well as for extracting physical information and predicting new phenomena.…”

Exactly solvable time-dependent pseudo-Hermitian su(1,1) Hamiltonian models

“…From a theoretical point view several efforts are yet necessary for a total comprehension and unifying description of dynamics related to time-dependent non-Hermitian Hamiltonians. Quite recently, proposals and investigations of fundamental issues have been done [26][27][28][29] and important physical aspects have been brought to light about time-dependent non-Hermitian Hamiltonians [31,32]. However, very few attempts are present in literature concerning the identification of classes of exactly solvable scenarios for physical systems described by time-dependent non-Hermitian Hamiltonians.…”