Statistics of eigenfunctions in open chaotic systems: a perturbative approach

Details Statistics of eigenfunctions in open chaotic systems: a perturbative approach Statistics of eigenfunctions in open chaotic systems: a perturbative approach

2009-06-30

arxiv.org/abs/0906.5611v2

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

Physics

Condensed Matter

Other Condensed Matter

Scientific paper

10.1103/PhysRevE.80.046203

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 r\^ole of spectral fluctuations.

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