Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the syste...Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.展开更多
We construct a family of dynamical systems whose evolution converges to the eigenvectors of a general square matrix, not necessarily symmetric. We analyze the convergence of those systems and perform numerical tests. ...We construct a family of dynamical systems whose evolution converges to the eigenvectors of a general square matrix, not necessarily symmetric. We analyze the convergence of those systems and perform numerical tests. Some examples and comparisons with the power methods are presented.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.62071248)the Natural Science Foundation of Nanjing University of Posts and Telecommunications(Grant No.NY223109)China Postdoctoral Science Foundation(Grant No.2022M721693).
文摘Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.
文摘We construct a family of dynamical systems whose evolution converges to the eigenvectors of a general square matrix, not necessarily symmetric. We analyze the convergence of those systems and perform numerical tests. Some examples and comparisons with the power methods are presented.
