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Level density for deformations of the Gaussian orthogonal ensemble
A C Bertuola1, J X de Carvalho, M S Hussein
1Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970 São Paulo, São Paulo, Brazil.
Summary
This study presents formulas for average level density in deformed Gaussian orthogonal random matrix ensembles. It covers transitions from the Gaussian orthogonal ensemble (GOE) to Poisson and multiple GOEs.
Area of Science:
- * Theoretical Physics
- * Quantum Chaos
- * Random Matrix Theory
Background:
- * Gaussian ensembles are fundamental in describing complex quantum systems.
- * Understanding level density is crucial for analyzing spectral fluctuations.
Purpose of the Study:
- * To derive formulas for the average level density of deformed Gaussian orthogonal random matrix ensembles.
- * To analyze the transition from the Gaussian orthogonal ensemble (GOE) to the Poisson ensemble.
- * To analyze the transition from the GOE to m GOEs.
Main Methods:
- * Derivation of analytical formulas for average level density.
- * Utilizing concepts from random matrix theory and statistical mechanics.
- * Analysis of ensemble transitions.
Main Results:
- * Formulas for average level density in transition ensembles are established.
- * Characterization of spectral properties during GOE-Poisson and GOE-mGOE transitions.
- * Provides a theoretical framework for deformed random matrix ensembles.
Conclusions:
- * The derived formulas offer new insights into the behavior of complex quantum systems.
- * This work extends the applicability of random matrix theory to deformed ensembles.
- * The findings are relevant for understanding spectral statistics in various physical contexts.