Statistics of eigenfunctions in open chaotic systems: a perturbative approach

2009/06/30 by Charles Poli, Dmitry Savin, Olivier Legrand +1 · 1 citation
Physics and Astronomy · #cond-mat.other #nlin.CD

paper · pdf · doi:10.1103/physreve.80.046203

published as Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 80 (2009) 046203

arxiv created 2009/11/10 · arxiv updated 2009/12/01

Abstract

We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated 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 rôle of spectral fluctuations.

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• Random Matrix Theory for Chaotic Wave Scattering and Transport

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