Related papers: Spectral statistics in chaotic systems with a poin…
We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in…
Quantum systems whose classical counterpart have ergodic dynamics are quantum ergodic in the sense that almost all eigenstates are uniformly distributed in phase space. In contrast, when the classical dynamics is integrable, there is…
We review recent studies about the resonance spectrum of quantum scattering systems, in the semiclassical limit and assuming chaotic classical dynamics. Stationary quantum properties are related to fractal structures in the classical phase…
It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we…
In the theory of disordered systems the spectral form factor $S(\tau)$, the Fourier transform of the two-level correlation function with respect to the difference of energies, is linear for $\tau<\tau_c$ and constant for $\tau>\tau_c$. Near…
We compare the statistical fluctuation properties of the baryon and meson experimental mass spectra with those obtained from theoretical models (quark models and lattice QCD). We find that for the experimental spectra the statistical…
We investigate quantised maps of the torus whose classical analogues are ergodic but not mixing. Their quantum spectral statistics shows non-generic behaviour, i.e.it does not follow random matrix theory (RMT). By coupling the map to a spin…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
The spectral correlation of a chaotic system with spin 1/2 is universally described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the semiclassical limit. In semiclassical theory, the spectral form factor is expressed in…
We study the universal fluctuations of the Wigner-Smith time delay for systems which exhibit chaotic dynamics in their classical limit. We present a new derivation of the semiclassical relation of the quantum time delay to properties of the…
Based on the connection between the spectral form factor and the probability to return, the origin of the $1/f^\alpha$-noise in fully chaotic and fully integrable systems is traced to the quantum interference between invariant manifolds of…
We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is simple enough to allow…
The statistical properties of speckle patterns have important applications in optics, oceanography, and transport phenomena in disordered systems. Here we obtain closed-form analytic results for the amplitude distribution of speckle…
Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
We study the level statistics of an interacting multi-qubit system, namely the kicked Ising spin chain, in the regime of quantum chaos. Long range quasi-energy level statistics show effects analogous to the ones observed in semi-classical…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck's constant, both classical and quantal distributions…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
Special quantum states exist which are quasiclassical quantizations of regions of phase space that are weakly chaotic. In a weakly chaotic region, the orbits are quite regular and remain in the region for some time before escaping and…