Bulk-Edge Correspondence for Nonlinear Eigenvalue Problems
Takuma Isobe, Tsuneya Yoshida, Yasuhiro Hatsugai
Abstract
Although topological phenomena attract growing interest not only in linear systems but also in nonlinear systems, the bulk-edge correspondence under the nonlinearity of eigenvalues has not been established so far. We address this issue by introducing auxiliary eigenvalues. We reveal that the topological edge states of auxiliary eigenstates are topologically inherited as physical edge states when the nonlinearity is weak but finite (i.e., auxiliary eigenvalues are monotonic as for the physical one). This result leads to the bulk-edge correspondence with the nonlinearity of eigenvalues.
Topics & Concepts
Eigenvalues and eigenvectorsNonlinear systemMonotonic functionEnhanced Data Rates for GSM EvolutionPhysicsStatistical physicsTopology (electrical circuits)MathematicsQuantum mechanicsMathematical analysisCombinatoricsComputer scienceTelecommunicationsTopological Materials and PhenomenaQuantum Mechanics and Non-Hermitian PhysicsMechanical and Optical Resonators