Geometric Phase in PT-Symmetric Quantum Mechanics

TL;DR

This paper explores a new class of adiabatic processes in PT-symmetric quantum mechanics, deriving a Berry-like phase that involves a fictitious monopole flux and string contributions, with implications for Hermitian systems.

Contribution

It introduces a novel geometric phase in PT-symmetric quantum systems with a time-dependent metric, expanding understanding of adiabatic evolution in non-Hermitian quantum mechanics.

Findings

Derived a Berry-like phase for PT-symmetric two-level systems.

Interpreted the phase as flux of a fictitious monopole with tunable charge.

Discussed the Hermitian analog of the PT-symmetric results.

Abstract

Unitary evolution in PT-symmetric quantum mechanics with a time-dependent metric is found to yield a new class of adiabatic processes. As an explicit example, a Berry-like phase associated with a PT-symmetric two-level system is derived and interpreted as the flux of a fictitious monopole with a tunable charge plus a singular string component with non-trivial phase contributions. The Hermitian analog of our results is also discussed.