Non-Hermiticity and Universality

Abstract

. We study the statistical properties of the eigenvalues of non-Hermitian operators assoicated with the dissipative complex systems. By considering the Gaussian ensembles of such operators, a hierarchical relation between the correlators is obtained. Further the eigenvalues are found to behave like particles moving on a complex plane under 2-body (inverse square) and 3-body interactions and there seems to underlie a deep connection and universality in the spectral behaviour of different complex systems. .

arXiv comment6 pages, No figures

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• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• Solvable scalar and spin models with near-neighbors interactions
• Random matrix ensembles with column/row constraints: part I
• Criticality in Brownian ensembles
• Random matrix ensembles with column/row constraints. II
• Eigenfunction statistics of Laguerre Brownian ensemble
• Spectral and Strength Statistics of Chiral Brownian Ensemble
• Statistical properties of power-law random banded unitary matrices in the delocalization-localization transition regime
• Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models