# Eigenvalue statistics for generalized symmetric and Hermitian matrices

@article{KumarDas2019EigenvalueSF, title={Eigenvalue statistics for generalized symmetric and Hermitian matrices}, author={Adway Kumar Das and Anandamohan Ghosh}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2019}, volume={52} }

Random matrix theory predicts the level statistics of a Hamiltonian to exhibit either clustering or repulsion if the underlying dynamics is integrable or chaotic, respectively. In various physical systems it is also possible to observe intermediate spectral properties showing the transition between different symmetry classes. In this work, we study generalized random matrix ensembles by dropping the constraint of canonical invariance and considering different variances in the diagonal and off…

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## References

SHOWING 1-10 OF 49 REFERENCES

### RANDOM MATRIX THEORY AND CHIRAL SYMMETRY IN QCD

- Physics
- 2000

▪ Abstract Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this…

### Crossover between the Gaussian orthogonal ensemble, the Gaussian unitary ensemble, and Poissonian statistics.

- PhysicsPhysical review. E
- 2017

An according formula for the level spacing distribution function depending on two parameters is proposed and it is proved that these crossovers are described reasonably and distinguish between regular and chaotic behavior as well as between existent or broken antiunitary symmetries.

### Random matrix physics: Spectrum and strength fluctuations

- Physics
- 1981

It now appears that the general nature of the deviations from uniformity in the spectrum of a complicated nucleus is essentially the same in all regions of the spectrum and over the entire Periodic…

### The energy level statistics of Hamiltonian systems between integrability and chaos: the semiclassical limit

- Physics, Mathematics
- 1996

### Wigner surmise for mixed symmetry classes in random matrix theory.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

Analytical formulas for the spacing distributions of 2×2 or 4×4 matrices are derived and it is shown how the coupling parameters of small and large matrices must be matched depending on the local eigenvalue density.

### Level clustering in the regular spectrum

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1977

In the regular spectrum of an f-dimensional system each energy level can be labelled with f quantum numbers originating in f constants of the classical motion. Levels with very different quantum…

### Reliability of small matrices for large spectra with nonuniversal fluctuations.

- MathematicsPhysical review letters
- 1991

To characterize the spectral changes of quantum spectra under two types of perturbations, a distribution of nearest-neighbor spacings is proposed, for each type of transition, and these ``generalized Wigner surmises'' are rigorous for suitable ensembles of 2-2 matrices but prove reliable for dynamical systems with many levels.

### Distribution of the ratio of consecutive level spacings in random matrix ensembles.

- MathematicsPhysical review letters
- 2013

The authors' Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit, and quantitative improvements are found through a polynomial expansion.

### Localization of interacting fermions at high temperature

- Physics
- 2007

We suggest that if a localized phase at nonzero temperature $Tg0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and…