Kubo formula for non-Hermitian systems and tachyon optical conductivity

TL;DR

This paper develops a generalized linear response theory and Kubo formula for non-Hermitian systems, revealing unique properties like finite dc conductivity in tachyon phases and broad applicability across various physical settings.

Contribution

It introduces a modified Kubo formula for non-Hermitian systems and applies it to a Dirac model with tachyonic excitations, uncovering novel transport phenomena.

Findings

Finite dc conductivity in tachyon phase

Exact optical sum rule satisfaction for all masses

Applicability of the theory to diverse non-Hermitian systems

Abstract

Linear response theory plays a prominent role in various fields of physics and provides us with extensive information about the thermodynamics and dynamics of quantum and classical systems. Here we develop a general theory for the linear response in non-Hermitian systems with non-unitary dynamics and derive a modified Kubo formula for the generalized susceptibility for arbitrary (Hermitian and non-Hermitian) system and perturbation. As an application, we evaluate the dynamical response of a non-Hermitian, one-dimensional Dirac model with imaginary and real masses, perturbed by a time-dependent electric field. The model has a rich phase diagram, and in particular, features a tachyon phase, where excitations travel faster than an effective speed of light. Surprisingly, we find that the dc conductivity of tachyons is finite, and the optical sum rule is exactly satisfied for all masses. Our results highlight the peculiar properties of the Kubo formula for non-Hermitian systems and are applicable for a large variety of settings.