相关论文: Localization in Strongly Chaotic Systems

We study the quantum localization in the chaotic eigenstates of a billiard with mixed-type phase space, after separating the regular and chaotic eigenstates, in the regime of slightly distorted circle billiard where the classical transport…

The fundamental correspondence between quantum chaotic single-particle systems and random matrix theory is well-understood via periodic orbit theory. In contrast, we show that many-body systems with explicit subsystem structure possess…

Matrix Models are the most effective way to describe strongly interacting systems with many degrees of freedom. They have proven successful in describing very different settings, from nuclei spectra to conduction in mesoscopic systems, from…

We use a Heisenberg spin-1/2 chain to investigate how chaos and localization may affect the entanglement of pairs of qubits. To measure how much entangled a pair is, we compute its concurrence, which is then analyzed in the…

A quantum system of particles can exist in a localized phase, exhibiting ergodicity breaking and maintaining forever a local memory of its initial conditions. We generalize this concept to a system of extended objects, such as strings and…

We address the decay in open chaotic quantum systems and calculate semiclassical corrections to the classical exponential decay. We confirm random matrix predictions and, going beyond, calculate Ehrenfest time effects. To support our…

In this paper, we study different types of phase space structures which appear in the context of relativistic chaotic scattering. By using the relativistic version of the H\'{e}non-Heiles Hamiltonian, we numerically study the topology of…

It is shown that the infinite random Heisenberg XXZ spin-$\frac12$ chain exhibits localization phenomena, such as spectral, eigenstate, and weak dynamical localization, in an arbitrary (but fixed) energy interval in a non-trivial region of…

By analyzing a paradigmatic example of the theory of dissipative systems -- the classical and quantum dissipative standard map -- we are able to explain the main features of the decay to the quantum equilibrium state. The classical…

Wave scattering in chaotic systems with a uniform energy loss (absorption) is considered. Within the random matrix approach we calculate exactly the energy correlation functions of different matrix elements of impedance or scattering…

The relaxation of out-of-time-ordered correlators (OTOCs) has been studied as a mean to characterize the scrambling properties of a quantum system. We show that the presence of local conserved quantities typically results in, at the…

The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…

Consider an n x n Hermitian random matrix with, above the diagonal, independent entries with alpha-stable symmetric distribution and 0 < alpha < 2. We establish new bounds on the rate of convergence of the empirical spectral distribution of…

We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some…

We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of "quantum chaotic dynamics". It is shown that under quite general conditions their roots…

Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that…

We show for the first time that a {\it weak} perturbation in a Hamiltonian system may lead to an arbitrarily {\it wide} chaotic layer and {\it fast} chaotic transport. This {\it generic} effect occurs in any spatially periodic Hamiltonian…

In a dynamical system the singular vector (SV) indicates which perturbation will exhibit maximal growth after a time interval $\tau$. We show that in systems with spatiotemporal chaos the SV exponentially localizes in space. Under a…

We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of…

We study the matrix elements of local and nonlocal operators in the single-particle eigenstates of two paradigmatic quantum-chaotic quadratic Hamiltonians; the quadratic Sachdev-Ye-Kitaev (SYK2) model and the three-dimensional Anderson…