Winding in Non-Hermitian Systems

Abstract

This paper extends the property of interlacing of the zeros of eigenfunctions in Hermitian systems to the topological property of winding number in non-Hermitian systems. Just as the number of nodes of each eigenfunction in a self-adjoint Sturm-Liouville problem are well-ordered, so too are the winding numbers of each eigenfunction of Hermitian and of unbroken PT-symmetric potentials. Varying a system back and forth past an exceptional point changes the windings of its eigenfunctions in a specific manner. Nonlinear, higher-dimensional, and general non-Hermitian systems also exhibit manifestations of these characteristics.

9 pages, 9 figures

References in corpus (1)

• Making Sense of Non-Hermitian Hamiltonians

Cited by in corpus (6)

• Non-Hermitian Topology and Exceptional-Point Geometries
• $\mathcal{P}T$ symmetry, pattern formation, and finite-density QCD
• PT-symmetric quantum graphs
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box
• Experimental Realization of Non-Abelian Permutations in a Three-State Non-Hermitian System