Non-Hermitian Model for Asymmetrical Tunneling

TL;DR

This paper introduces a simple non-Hermitian model that explains asymmetric tunneling between degenerate sites with non-reciprocal coupling, showing that such systems can reach unequal occupation states without dissipation.

Contribution

The paper develops a non-Hermitian framework using biorthogonal eigenvectors to model asymmetric tunneling, highlighting a novel approach to non-reciprocal quantum dynamics.

Findings

Tunneling rates are asymmetric in the model.

System reaches equilibrium with unequal occupation.

Unitarity is effectively restored through normalization.

Abstract

We present a simple non-hermitian model to describe the phenomenon of asymmetric tunneling between two energy-degenerate sites coupled by a non-reciprocal interaction without dissipation. The system was described using a biorthogonal family of energy eigenvectors, the dynamics of the system was determined by the Schr\"odinger equation, and unitarity was effectively restored by proper normalization of the state vectors. The results show that the tunneling rates are indeed asymmetrical in this model, leading to an equilibrium that displays unequal occupation of the degenerate systems even in the absence of external interactions.