Spectra and transport of probability and energy densities in a $\mathcal{PT}$-symmetric square well with a delta-function potential

TL;DR

This paper investigates the spectral, eigenstate, and transport characteristics of a $ ext{PT}$-symmetric square well with a delta potential, revealing exceptional points and efficient transport in the symmetric phase.

Contribution

It introduces a simple $ ext{PT}$-symmetric model with a delta potential, analyzing its spectral properties, exceptional points, and transport behavior, which advances understanding of non-Hermitian quantum systems.

Findings

Exceptional points occur with increasing delta potential strength.

Transport is efficient in the $ ext{PT}$-symmetric phase.

A generalized unitary relation for transmission and reflection is derived.

Abstract

We study the spectrum, eigenstates and transport properties of a simple $\mathcal{P}\mathcal{T}$-symmetric model consisting in a finite, complex, square well potential with a delta potential at the origin. We show that as the strength of the delta potential increases, the system exhibits exceptional points accompanied by an accumulation of density associated with the break in the $\mathcal{P}\mathcal{T}$-symmetry. We also obtain the density and energy density fluxes and analyze their transport properties. We find that in the $\mathcal{P}\mathcal{T}-$ symmetric phase transport is efficient, in the sense that all the density that flows into the system at the source, flows out at the sink, which is sufficient to derive a generalized unitary relation for the transmission and reflection coefficients.