Statistics of eigenfunctions in open chaotic systems: a perturbative approach

Charles Poli (1) , Dmitry Savin (2) , Olivier Legrand (1) , Fabrice Mortessagne (1)

1 LPMC - Laboratoire de physique de la matière condensée
2 DEPARTMENT OF MATHEMATICAL SCIENCES - Department of Mathematical Sciences

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.

Domaines: Autre [cond-mat.other]; Dynamique Chaotique [nlin.CD]

Charles Poli, Dmitry Savin, Olivier Legrand, Fabrice Mortessagne. Statistics of eigenfunctions in open chaotic systems: a perturbative approach. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2009, 80, pp.046203. ⟨10.1103/PhysRevE.80.046203⟩. ⟨hal-00400454v2⟩