Nearest level spacing statistics in open chaotic systems: a generalization of the Wigner Surmise
arXiv:1201.5096 · doi:10.1103/PhysRevLett.108.174101
Abstract
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 modifications on the spacing distributions produced by the coupling to the environment. Based on the analytical expressions obtained, we then propose general expressions of the spacing distributions for any number of channels, valid from weak to strong coupling. The latter expressions contain one free parameter. The surmise is successfully compared with numerical simulations of non-Hermitian random matrices and with experimental data obtained with a lossy electromagnetic chaotic cavity.
References in corpus (6)
- Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
- Universal Statistics of the Scattering Coefficient of Chaotic Microwave Cavities
- Trace formula for dielectric cavities II: Regular, pseudo-integrable, and chaotic examples
- Inhomogeneous losses and complexness of wave functions in chaotic cavities
- Statistics of eigenfunctions in open chaotic systems: a perturbative approach
- Avoided level crossing statistics in open chaotic billiards
Cited by in corpus (12)
- Leaking Chaotic Systems
- Spectral properties of microwave graphs with local absorption
- Weyl asymptotics: From closed to open systems
- Level statistics of extended states in random non-Hermitian Hamiltonians
- Wave Chaos in a Cavity of Regular Geometry with Tunable Boundaries
- Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial field
- GOE statistics in graphene billiards with the shape of classically integrable billiards
- Formation and interaction of resonance chains in the open 3-disk system
- Experimental investigation of the elastic enhancement factor in a transient region between regular and chaotic dynamics
- Wave systems with direct processes and localized losses or gains: the non-unitary Poisson kernel
- Cross section versus time delay and trapping probability
- Level dynamics and avoided level crossings in driven disordered quantum dots