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Statistics of resonance states in open chaotic systems: a perturbative approach

, : Statistics of resonance states in open chaotic systems: a perturbative approach. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 80(4 Pt 2): 046203-046203

We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (nonorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of weakly overlapping resonances, we apply the random matrix theory to the effective Hamiltonian formalism and derive analytically the probability distribution of the complexness parameter for two statistical ensembles describing the systems invariant under time reversal. For those with rigid spectra, we consider a Hamiltonian characterized by a picket-fence spectrum without spectral fluctuations. Then, in the more realistic case of a Hamiltonian described by the Gaussian orthogonal ensemble, we reveal and discuss the role of spectral fluctuations.


PMID: 19905411

DOI: 10.1103/PhysRevE.80.046203

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