Non-Hermitian β-ensemble with real eigenvalues
نویسندگان
چکیده
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 کاملThe real Ginibre ensemble with k = O(n) real eigenvalues
We consider the ensemble of real Ginibre matrices conditioned to have positive fraction α > 0 of real eigenvalues. We demonstrate a large deviations principle for the joint eigenvalue density of such matrices and introduce a two phase log-gas whose stationary distribution coincides with the spectral measure of the ensemble. Using these tools we provide an asymptotic expansion for the probabilit...
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 کاملNon-Hermitian Hamiltonians with real and complex eigenvalues: An sl(2,C) approach
Potential algebras are extended from Hermitian to non-Hermitian Hamiltonians and shown to provide an elegant method for studying the transition from real to complex eigenvalues for a class of non-Hermitian Hamiltonians associated with the complex Lie algebra A1.
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: AIP Advances
سال: 2013
ISSN: 2158-3226
DOI: 10.1063/1.4796167