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We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
We calculate the power spectrum of vacuum fluctuations of a generic scalar field in a quantum cosmological setting that is manifestly singularity-free. The power spectrum is given in terms of the usual scale invariant spectrum plus scale…
We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by Random Matrix Theory. We demonstrate it by…
In this paper we investigate system identification for general quantum linear systems. We consider the situation where the input field is prepared as stationary (squeezed) quantum noise. In this regime the output field is characterised by…
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…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…
Parametric correlations of energy spectra of quantum chaotic systems are presented in the orthogonal-unitary and symplectic-unitary crossover region. The spectra are allowed to disperse as a function of two external perturbations: one of…
The quantum ratchet effect in fully chaotic systems is approached by studying, for the first time, \emph{statistical} properties of the ratchet current over well-defined sets of initial states. Natural initial states in a semiclassical…
Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and…
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…
Chaotic behavior or lack thereof in non-Hermitian systems is often diagnosed via spectral analysis of associated complex eigenvalues. Very recently, singular values of the associated non-Hermitian systems have been proposed as an effective…
We derive a set of spectral statistics whose power spectrum is characterized, in the case of chaotic quantum systems, by colored noise $1/f^{\gamma}$, where the integer parameter $\gamma$ critically depends on the specific energy-level…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
The spectral statistic $\delta_n$ measures the fluctuations of the number of energy levels around its mean value. It has been shown that chaotic quantum systems display $1/f$ noise (pink noise) in the power spectrum $S(f)$ of the $\delta_n$…
We study the $n$-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit's universality conjecture, it is expected that the correlation functions…
Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting…
The power spectrum is a Fourier series statistic associated with the covariances of the displacement from average positions of the members of an eigen-sequence. When this eigen-sequence has rotational invariance, as for the eigen-angles of…
In this article we investigate no-resonance conditions for quantum many body chaotic systems and random matrix models. No-resonance conditions are properties of the spectrum of a model, usually employed as a theoretical tool in the analysis…
A set of zero-range scatterers along its axis lifts the integrability of a harmonic waveguide. Effective solution of the Schr\"odinger equation for this model is possible due to the separable nature of the scatterers and millions of…