What is the resonant state in open quantum systems?

TL;DR

This paper reviews the theory of resonant states in open quantum systems, focusing on non-Hermiticity, complex eigenvalues, and the physical interpretation of these states, including their formation and properties.

Contribution

It provides a comprehensive overview of the non-Hermitian framework for open quantum systems and introduces the Feshbach formalism as an alternative method to identify resonant states.

Findings

Resonant states have complex eigenvalues with physical significance.

Non-Hermiticity explains peak structures in scattering and transport.

Feshbach formalism offers an effective way to find resonant states.

Abstract

The article reviews the theory of open quantum system from a perspective of the non-Hermiticity that emerges from the environment with an infinite number of degrees of freedom. The non-Hermiticity produces resonant states with complex eigenvalues, resulting in peak structures in scattering amplitudes and transport coefficients. After introducing the definition of resonant states with complex eigenvalues, we answer typical questions regarding the non-Hermiticity of open quantum systems. What is the physical meaning of the complex eigenmomenta and eigenenergies? How and why do the resonant states break the time-reversal symmetry that the system observes? Can we make the probabilistic interpretation of the resonant states with diverging wave functions? What is the physical meaning of the divergence of the wave functions? We also present an alternative way of finding resonant states, namely the Feshbach formalism, in which we eliminate the infinite number of the environmental degrees of freedom. In this formalism, we attribute the non-Hermiticity to the introduction of the retarded and advanced Green's functions.