Winding around Non-Hermitian Singularities: General Theory and Topological Features
arXiv:1805.07620
Abstract
Non-Hermitian singularities are ubiquitous in non-conservative open systems. These singularities are often points of measure zero in the eigenspectrum of the system which make them difficult to access without careful engineering. Despite that, they can remotely induce observable effects when some of the system's parameters are varied along closed trajectories in the parameter space. To date, a general formalism for describing this process beyond simple cases is still lacking. Here, we bridge this gap and develop a general approach for treating this problem by utilizing the power of permutation operators and representation theory. This in turn allows us to reveal the following surprising result which contradicts the common belief in the field: loops that enclose the same singularities starting from the same initial point and traveling in the same direction, do not necessarily share the same end outcome. Interestingly, we find that this equivalence can be formally established only by invoking the topological notion of homotopy. Our findings are general with far reaching implications in various fields ranging from photonics and atomic physics to microwaves and acoustics.
References in corpus (12)
- Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
- Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
- Topological energy transfer in an optomechanical system with exceptional points
- Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
- Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
- Dynamically encircling exceptional points: Exact evolution and polarization state conversion
- Exceptional Points in Atomic Spectra
- Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
- Exceptional Points in a Non-Hermitian Topological Pump
- Analysis of multiple exceptional points related to three interacting eigenmodes in a non-Hermitian Hamiltonian
- Supersymetric laser arrays
- Non-Hermitian engineering of single mode two dimensional laser arrays