PT-Symmetric SU(2) - like Random Matrix Ensembles: Invariant Distributions and Spectral Fluctuations
Year: 2025
Type: article
Abstract: We consider an ensemble of $$2\times 2$$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining probability distributions based on symmetry and statistical independence. The probability densities turn out to be power law with exponents that depend on the boundedness of the domain. For small spacings, $$\sigma $$ , the probability density varies as $$\sigma ^{\nu }$$ , $$\nu \ge 2$$ . The degree of level repulsion is a parameter of great interest as it makes a connection to quantum chaos; the lower bound of $$\nu $$ for our ensemble coincides with the Gaussian Unitary Ensemble. We believe that the systematic development presented here paves the way for further generalizations in the field of random matrix theory for PT-symmetric quantum systems.
Authors: Stalin Abraham, A. Bhagwat, Sudhir Ranjan Jain
Institutions: University of Mumbai, Center for Excellence in Basic Sciences
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4409814541