Consistency between adiabatic and nonadiabatic geometric phases for nonselfadjoint hamiltonians

TL;DR

This paper investigates the apparent inconsistency in geometric phase calculations for nonselfadjoint Hamiltonians under adiabatic approximation, showing that differences are balanced by deviations in dynamical phases.

Contribution

It clarifies the relationship between adiabatic and nonadiabatic geometric phases for nonselfadjoint Hamiltonians, resolving a previously observed inconsistency.

Findings

Two different expressions for geometric phase are shown to be consistent when accounting for dynamical phase deviations.

The discrepancy between adiabatic and nonadiabatic phases is explained by small dynamical phase corrections.

The study enhances understanding of geometric phases in non-Hermitian quantum systems.

Abstract

We show that the adiabatic approximation for nonselfadjoint hamiltonians seems to induce two non-equal expressions for the geometric phase. The first one is related to the spectral projector involved in the adiabatic theorem, the other one is the adiabatic limit of the nonadiabatic geometric phase. This apparent inconsistency is resolved by observing that the difference between the two expressions is compensated by a small deviation in the dynamical phases.