Related papers: Circular unitary ensemble with highly oscillatory …
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
We study the influence of reflective boundaries on time-dependent responses of one-dimensional quantum fluids at zero temperature beyond the low-energy approximation. Our analysis is based on an extension of effective mobile impurity models…
In this paper we study in detail the localized wave functions defined in Phys. Rev. Lett. {\bf 76}, 1613 (1994), in connection with the scarring effect of unstable periodic orbits in highly chaotic Hamiltonian system. These functions appear…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
We show that the limiting eigenvalue density of the product of n identically distributed random matrices from an isotropic unitary ensemble (IUE) is equal to the eigenvalue density of n-th power of a single matrix from this ensemble, in the…
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we…
Non-universal correlations due to localization are observed in statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities. Varying energy {E} and mean free path {l} enable us to experimentally…
In this paper we calculate, in the large N limit, the eigenvalue density of an infinite product of random unitary matrices, each of them generated by a random hermitian matrix. This is equivalent to solving unitary diffusion generated by a…
Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices…
We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
The strong nature of Composite Higgs models manifests at high energies through the growing behavior of the scattering amplitudes of longitudinally polarized weak bosons that leads to the formation of composite resonances as well as…
We analyze the observed distribution of the orbital eccentricity and period of binary radio pulsars in globular clusters using computational tools to simulate binary-single star interactions. Globular clusters have different groups of…
Motivated by the importance ascribed to correlations in random matrices used to model phenomena in various scientific disciplines, we report how algebraic correlations between matrix elements affect the eigenvalue statistics and spectral…
We examine theoretically the effects caused by a periodic external potential on the correlated motion of a two-dimensional electron system under strong magnetic fields corresponding to a filling factor 1/2. To describe the resulting complex…
Periodic orbits in chaotic systems form clusters, whose elements traverse approximately the same points of the phase space. The distribution of cluster sizes depends on the length n of orbits and the parameter p which controls closeness of…
We investigate the scattering properties of one-dimensional, periodically and non-periodically forced oscillators. The pattern of singularities of the scattering function, in the periodic case, shows a characteristic hierarchical structure…
The $M$-dimensional unitary matrix $S(E)$, which describes scattering of waves, is a strongly fluctuating function of the energy for complex systems such as ballistic cavities, whose geometry induces chaotic ray dynamics. Its statistical…