Related papers: Eigenstate Correlations in Dual-Unitary Quantum Ci…
We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on…
Physical systems are often neither completely closed nor completely open, but instead they are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main…
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…
We consider a classically chaotic system that is described by an Hamiltonian $H(Q,P;x)$ where x is a constant parameter. Our main interest is in the case of a gas-particle inside a cavity, where $x$ controls a deformation of the boundary or…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
We review recent studies about the resonance spectrum of quantum scattering systems, in the semiclassical limit and assuming chaotic classical dynamics. Stationary quantum properties are related to fractal structures in the classical phase…
Quasi-one-dimensional quantum structures with spectra scaling faster than the square of the eigenmode number (superscaling) can generate intrinsic, off-resonant optical nonlinearities near the fundamental physical limits, independent of the…
Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit…
We consider a minimal model for quantum thermalization of coupled chaotic subsystems. The route towards ergodicity is explored as a function of the coupling strength. The results are contrasted with the predictions of standard Random Matrix…
In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the…
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide…
We propose a possible resolution for the problem of why the semicircular law is not observed, whilst the random matrix hypothesis describes well the fluctuation of energy spectra. We show in the random 2-matrix model that the interactions…
This paper is devoted to the statistics of the quantum eigenfunctions in an ensemble of finite disordered systems (metallic grains). We focus on moments of inverse participation ratio. In the universal random matrix limit that corresponds…
The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
Correspondence in quantum chaotic systems is lost in short time scales. Introducing some noise we study the spectrum of the resulting coarse grained propagaor of density matrices. Some differen methods to compute the spectrum are reviewed.…
Interacting many-body systems with explicitly accessible spatio-temporal correlation functions are extremely rare, especially in the absence of integrability. Recently, we identified a remarkable class of such systems and termed them…
Using the Bargmann-Husimi representation of quantum mechanics on a torus phase space, we study analytically eigenstates of quantized cat maps. The linearity of these maps implies a close relationship between classically invariant…
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…