Geometric-phase effects accumulated by the dynamical-phase differences in non-Hermitian systems
Phys. Rev. A 113, 012227 – Published 27 January, 2026
DOI: https://doi.org/10.1103/sprq-fmgr
Abstract
We rederive and investigate different Berry connection forms of non-Hermitian systems from several fundamental aspects. This enables us to obtain a form of Berry connection in pure right-vector representation, which is distinguishable from the usual Berry connection expressed by right vectors in previous works. Then the relations and differences among the distinct Berry connection forms are discussed systemically through observations of complex geometric phases based on piecewise adiabatic evolution. We find a striking quantitative relation , which predicts that the cumulative minute energy differences (between the time-dependent energy expectation value and the instantaneous eigenvalue during an adiabatic process, ) manifest as geometric phases () uniquely in non-Hermitian systems. We further propose a scheme leveraging soliton dynamics in dissipative two-component Bose-Einstein condensates, enabling direct measurement of these topological signatures. These results establish a milestone for understanding Dirac monopole charge distributions and measuring complex geometric phases in non-Hermitian systems, with far-reaching implications for non-Hermitian photonics.
