Real eigenvalues are determined by the recursion of eigenstates
- URL: http://arxiv.org/abs/2309.09418v1
- Date: Mon, 18 Sep 2023 01:30:09 GMT
- Title: Real eigenvalues are determined by the recursion of eigenstates
- Authors: Tong Liu and Youguo Wang
- Abstract summary: We show that real eigenvalues can emerge under the appropriate recursion condition of eigenstates.
Our findings provide another path to extract the real energy spectrum of non-Hermitian systems.
- Score: 5.8411054896644
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum physics is generally concerned with real eigenvalues due to the
unitarity of time evolution. With the introduction of $\mathcal{PT}$ symmetry,
a widely accepted consensus is that, even if the Hamiltonian of the system is
not Hermitian, the eigenvalues can still be pure 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.
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