Pseudo-Hermitian random matrix theory

Abstract

Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present applications to problems in statistical mechanics where new results have become possible. We have found it important to mention the precise directions where advances could be made if further results become available.

References in corpus (15)

• Chaos and Quantum Thermalization
• Complex Extension of Quantum Mechanics
• Pseudo-Hermitian Representation of Quantum Mechanics
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Eigenvalue statistics of the real Ginibre ensemble
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• Coulomb analogy for nonhermitian degeneracies near quantum phase transitions
• Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
• Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices
• From PT-symmetric quantum mechanics to conformal field theory
• Quantum chaos, random matrix theory, and statistical mechanics in two dimensions - a unified approach
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• Random cyclic matrices
• Nuclear Structure and the Search for Collective Enhancement of P,T-Violation
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions

Cited by in corpus (5)

• Random matrix ensembles for $PT$-symmetric systems
• Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices
• Pseudo-Hermitian and PT -symmetric quantum systems with energy-dependent potentials: Bound-state solutions and energy spectra
• Spectral statistics of interpolating random circulant matrix and its applications to random circulant graphs
• Entanglement of pseudo-Hermitian random states