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Pseudo-Hermitian ensemble of random Gaussian matrices
1Instituto de Física, Rua do Matão 1371, Universidade de São Paulo, 05508-090, São Paulo, S.P., Brazil.
Physical Review. E
|August 31, 2016
Summary
Pseudo-Hermiticity is introduced into random matrix theory, enabling the study of PT symmetric systems. This reveals transitions where eigenvalues shift from real to complex conjugate pairs.
Area of Science:
- Quantum mechanics
- Random matrix theory
- Mathematical physics
Background:
- Pseudo-Hermiticity is crucial for parity-time (PT) symmetric quantum systems.
- Random matrix theory provides a framework for analyzing complex quantum systems.
Purpose of the Study:
- To investigate the introduction of pseudo-Hermiticity within the three Gaussian classes of random matrix theory.
- To model the transition of eigenvalues from real to complex conjugate states.
Main Methods:
- Incorporating pseudo-Hermiticity into the Gaussian ensembles of random matrix theory.
- Analyzing the spectral properties of the modified random matrix models.
Main Results:
- Demonstrated the successful integration of pseudo-Hermiticity into random matrix theory.
- Observed a transition from purely real eigenvalues to a spectrum with complex conjugate pairs, alongside a residual real eigenvalue set.
Conclusions:
- Pseudo-Hermiticity can be effectively modeled within random matrix theory.
- The study provides insights into the spectral behavior of PT symmetric systems and their transitions.
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