Level statistics of real eigenvalues in non-Hermitian systems
نویسندگان
چکیده
Time-reversal symmetry and pseudo-Hermicity are shown to lead five universal level statistics of real eigenvalues non-Hermitian systems, using random matrix theory analyses numerical diagonalizations.
منابع مشابه
Classes of non-Hermitian operators with real eigenvalues
Classes of non-Hermitian operators that have only real eigenvalues are presented. Such operators appear in quantum mechanics and are expressed in terms of the generators of the Weyl-Heisenberg algebra. For each non-Hermitian operator A, a Hermitian involutive operator Ĵ such that A is Ĵ-Hermitian, that is, ĴA = AĴ , is found. Moreover, we construct a positive definite Hermitian Q such that A is...
متن کاملEla Classes of Non-hermitian Operators with Real Eigenvalues
Classes of non-Hermitian operators that have only real eigenvalues are presented. Such operators appear in quantum mechanics and are expressed in terms of the generators of the Weyl-Heisenberg algebra. For each non-Hermitian operator A, a Hermitian involutive operator Ĵ such that A is Ĵ-Hermitian, that is, ĴA = AĴ , is found. Moreover, we construct a positive definite Hermitian Q such that A is...
متن کاملNon-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
We show that complex Lie algebras (in particular sl(2,C)) provide us with an elegant method for studying the transition from real to complex eigenvalues of a class of non-Hermitian Hamiltonians: complexified Scarf II, generalized Pöschl-Teller, and Morse. The characterizations of these Hamiltonians under the so-called pseudoHermiticity are also discussed. PACS: 02.20.Sv; 03.65.Fd; 03.65.Ge
متن کاملAcceleration of the Arnoldi method and real eigenvalues of the non-Hermitian Wilson-Dirac operator
In this paper, we present a method for the computation of the low-lying real eigenvalues of the Wilson-Dirac operator based on the Arnoldi algorithm. These eigenvalues contain information about several observables. We used them to calculate the sign of the fermion determinant in oneflavor QCD and the sign of the Pfaffian in N = 1 super Yang-Mills theory. The method is based on polynomial transf...
متن کاملStructure of trajectories of complex-matrix eigenvalues in the Hermitian-non-Hermitian transition.
The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical review research
سال: 2022
ISSN: ['2643-1564']
DOI: https://doi.org/10.1103/physrevresearch.4.043196