Related papers: Hyperbolic disordered ensembles of random matrices
Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…
We continue the development of a so called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric $\cos$-interference,…
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 analytically study spectral correlations and many body wave functions of an SYK-model deformed by a one body contribution to the Hamiltonian. Our main result is the identification of a wide range of intermediate coupling strengths where…
We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…
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…
Chaotic behavior of quantum systems can be characterized by the adherence of the expectation values of given probes to moments of the Haar distribution. In this work, we analyze the behavior of several probes of chaos using a technique…
We study the eigenvalues and the eigenvectors of $N\times N$ structured random matrices of the form $H = W\tilde{H}W+D$ with diagonal matrices $D$ and $W$ and $\tilde{H}$ from the Gaussian Unitary Ensemble. Using the supersymmetry technique…
We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as model for the low-temperature vibrational properties of glass. Exact…
Superbosonization is a new variant of the method of commuting and anti-commuting variables as used in studying random matrix models of disordered and chaotic quantum systems. We here give a concise mathematical exposition of the key…
Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or, well-known number sequences may display strong signatures that the Hamiltonian yielding them as eigenvalues is…
We construct a family of chaotic dynamical systems with explicit broad distributions, which always violate the central limit theorem. In particular, we show that the superposition of many statistically independent, identically distributed…
We consider non-interacting bosonic excitations in disordered systems, emphasising generic features of quadratic Hamiltonians in the absence of Goldstone modes. We discuss relationships between such Hamiltonians and the symmetry classes…
In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parametrized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
The remarkable universality of the eigenvalue correlation functions is perhaps one of the most salient findings in random matrix theory. Particularly for short-range separations of the eigenvalues, the correlation functions have been shown…
A generalized Hubbard-Stratonovitch transformation relating an integral over random unitary N times N matrices to an integral over Efetov's unitary sigma model manifold, is introduced. This transformation adapts the supersymmetry method to…
We introduce the concept of $\epsilon$-uncontrollability for random linear systems, i.e. linear system in which the usual matrices have been replaced by random matrices. We also estimate the $\epsilon$-uncontrollability in the case where…
When an integrable two-degrees-of-freedom Hamiltonian system possessing a circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It is proved that its occurrence is generic for one parameter families (co-dimension one…