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abstract: '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.'
author:
- Charles Poli
- 'Dmitry V. Savin'
- Olivier Legrand
- Fabrice Mortessagne
title: 'Statistics of resonance states in open chaotic systems: A perturbative approach'
---

Introduction
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In the domain of wave or quantum chaos [@Sto99], open systems are currently actively investigated both from experimental and theoretical points of view (see Refs. [@Kuh05; @Fyo05] for recent reviews). Openness may be due to various physical mechanisms such as bulk absorption, coupling to the environment through physical channels as well as dissipative or radiative boundary conditions. Whatever the mechanism, openness results in spectral broadening ranging from 