Generalized Unitarity Relation for Linear Scattering Systems in One Dimension

TL;DR

This paper derives a generalized unitarity relation applicable to a wide range of linear scattering systems, including those that violate traditional symmetries like unitarity and reciprocity.

Contribution

It introduces a unitarity relation that extends to non-Hermitian and non-reciprocal linear scattering systems, broadening theoretical understanding.

Findings

Derived a generalized unitarity relation for arbitrary linear scattering systems.

Applicable to systems violating unitarity, time-reversal, and ${ m PT}$-symmetry.

Provides a theoretical framework for analyzing complex scattering phenomena.

Abstract

We derive a generalized unitarity relation for an arbitrary linear scattering system that may violate unitarity, time-reversal invariance, ${\cal PT}$-symmetry, and transmission reciprocity.