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The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary and a chaos producing part. The Gaussian…
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…
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…
Statistical aspects of the dynamics of chaotic scattering in the classical model of $\alpha$-cluster nuclei are studied. It is found that the dynamics governed by hyperbolic instabilities which results in an exponential decay of the…
We study the effect of gradual symmetry breaking in a non-integrable system on the level fluctuation statistics. We consider the case when the symmetry is represented by a quantum number that takes one of two possible values, so that the…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $\sigma$--model…
Level fluctuations in quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate level fluctuations to the classical dynamics in the regular and chaotic limit. In…
In the Coulomb blockade regime of a ballistic quantum dot, the distribution of conductance peak spacings is well known to be incorrectly predicted by a single-particle picture; instead, matrix element fluctuations of the residual electronic…
We study the interplay between regular and chaotic dynamics at the critical point of a generic first-order quantum phase transition in an interacting boson model of nuclei. A classical analysis reveals a distinct behavior of the coexisting…
We present a robust analysis of the spectral fluctuations exhibited by the light meson spectrum. This analysis provides information about the degree of chaos in light mesons and may be useful to get some insight on the underlying…
The spectral fluctuation properties of spherical nuclei are considered by use of NNSD statistic. With employing a generalized Brody distribution included Poisson, GOE and GUE limits and also MLE technique, the chaoticity parameters are…
The two-nucleon spectral function in nuclear matter is studied using Correlated Basis Function perturbation theory, including central and tensor correlations produceded by a realistic hamiltonian. The factorization property of the…
The Floquet operator, defined as the time-evolution operator over one period, plays a central role in the work presented in this thesis on periodically perturbed quantum systems. Knowledge of the spectral nature of the Floquet operator…
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…
Statistical fluctuations of the nuclear ground state energies are estimated using shell model calculations in which particles in the valence shells interact through well defined forces, and are coupled to an upper shell governed by random…
Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed…
New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point…
We investigate the low-lying spectra of many-body systems with random two-body interactions, specifying that the ensemble be invariant under particle-hole conjugation.Surprisingly we find patterns reminiscent of more orderly interactions,…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…