Definition of Current Density in Non-Hermitian Quantum Systems

Abstract

In recent years, non-Hermitian quantum systems (NHQS) have been actively studied. In conventional quantum mechanics, Hermiticity is a fundamental property of Hamiltonians. In NHQS, however, states evolve under non-Hermitian Hamiltonians and novel physical phenomena are predicted due to the non-Hermiticity. One difference from Hermitian systems is that the continuity equation (CE) does not hold in NHQS even when the number of particles is conserved. In this study, I extended the definition of current density so that CE holds also in NHQS. The newly defined current density does not only satisfy CE but also has physical meanings in the sense that it affects physical observables in the same manner as conventional current density.