Randomly incomplete spectra and intermediate statistics
arXiv:cond-mat/0608165 · doi:10.1103/PhysRevE.74.036212
Abstract
By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix theory (RMT) spectra and picket fence spectra. It is shown that the Fredholm determinant formalism of RMT extends naturally to describe incomplete RMT spectra.
9 pages, 2 figures. To appear in Physical Review E
References in corpus (12)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
- Periodic-Orbit Theory of Universality in Quantum Chaos
- New Class of Random Matrix Ensembles with Multifractal Eigenvectors
- Universal Spectral Correlations at the Mobility Edge
- Quantum Chaotic Dynamics and Random Polynomials
- A generalized ensemble of random matrices
- Missing levels in correlated spectra
- Critical statistics in quantum chaos and Calogero-Sutherland model at finite temperature
- Nearest-neighbor distribution for singular billiards
- Daisy Models: Semi-Poisson statistics and beyond
- Random polynomials, random matrices, and -functions
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