ﻻ يوجد ملخص باللغة العربية
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.
We investigate the nearest level spacing statistics of open chaotic wave systems. To this end we derive the spacing distributions for the three Wigner ensembles in the one-channel case. The theoretical results give a clear physical meaning of the mod
In this letter, we demonstrate that a non-Hermitian Random Matrix description can account for both spectral and spatial statistics of resonance states in a weakly open chaotic wave system with continuously distributed losses. More specifically, the s
The interest in the properties of quantum systems, whose classical dynamics are chaotic, derives from their abundance in nature. The spectrum of such systems can be related, in the semiclassical approximation (SCA), to the unstable classical periodic
Perturbation theory (PT) is a powerful and commonly used tool in the investigation of closed quantum systems. In the context of open quantum systems, PT based on the Markovian quantum master equation is much less developed. The investigation of open
We present a perturbative model for crystal-field calculations, which keeps into account the possible mixing of states labelled by different quantum number J. Analytical J-mixing results are obtained for a Hamiltonian of cubic symmetry and used to in