Related papers: Universality classes of quantum chaotic dissipativ…
Random matrix models consisting of normal matrices, defined by the sole constraint $[N^{\dag},N]=0$, will be explored. It is shown that cubic eigenvalue repulsion in the complex plane is universal with respect to the probability…
We study statistical properties of energy spectra of a tight-binding model on the two-dimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of finite approximants, we find that the underlying universal…
We investigate coherent multiple scattering effects in the random quantum kicked rotor model. By changing the starting time of the Floquet period, two new classes of models can be introduced that exhibit similar interference structures. For…
We consider the universality of the nearest neighbour eigenvalue spacing distribution in invariant random matrix ensembles. Focussing on orthogonal and symplectic invariant ensembles, we show that the empirical spacing distribution…
We compute the full probability distribution of the spectral form factor in the self-dual kicked Ising model by providing an exact lower bound for each moment and verifying numerically that the latter is saturated. We show that at large…
We discuss the roles of the macroscopic limit and of different system-environment interactions in the quantum-classical transition for a chaotic system. We consider the kicked harmonic oscillator subject to reservoirs that correspond in the…
We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic…
We show that introducing a localized leak in Floquet systems with time-reversal symmetry leads to universal spectral correlations governed by the non-Hermitian symmetry class $\mathrm{AI}^{\dagger}$, associated with complex-symmetric…
The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal…
Introducing a class of SU(2) invariant quantum unitary circuits generating chiral transport, we examine the role of broken space-reflection and time-reversal symmetries on spin transport properties. Upon adjusting parameters of local…
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study…
It is commonly expected that for quantum chaotic many body systems, the statistical properties approach those of random matrices when increasing the system size. We demonstrate for various kicked spin-1/2 chain models that the average…
Recently, S\'a, Ribeiro and Prosen introduced complex spacing ratios to analyze eigenvalue correlations in non-Hermitian systems. At present there are no analytical results for the probability distribution of these ratios in the limit of…
We show that non-Hermitian Ginibre random matrix behaviors emerge in spatially-extended many-body quantum chaotic systems in the space direction, just as Hermitian random matrix behaviors emerge in chaotic systems in the time direction.…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
This paper concerns with the time-reversal characteristics of intrinsic normal diffusion in quantum systems. Time-reversible properties are quantified by the time-reversal test; the system evolved in the forward direction for a certain…
The response of dissipative systems to multi-chromatic fields exhibits generic properties which follow from the discrete time-translation symmetry of each driving component. We derive these properties and illustrate them with paradigmatic…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball…
Quantum many-body systems are commonly considered as quantum chaotic if their spectral statistics, such as the level spacing distribution, agree with those of random matrix theory. Using the example of the kicked Ising chain we demonstrate…