Related papers: Spectral Statistics and Dynamical Localization: sh…
We use tools based on the modern theory of polarization for a numerical study of the localization transition of the Aubry-Andr\'{e} model. In this model the spatial modulation of the potential, $\alpha$, is an irrational number, which we…
We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional billiard systems with corners. This is achieved by using the exact Sommerfeld solution for the Green…
A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics whereas those of time-reversal symmetric,…
We consider a modification of isospectral cavities whereby the classical dynamics changes from pseudointegrable to chaotic. We construct an example where we can prove that isospectrality is retained. We then demonstrate this explicitly in…
We study level correlations in a two-dimensional system with a long-range random potential and strong spin-orbit (SO) splitting of the spectrum. The level correlations for sufficiently large splitting are shown to be described by orthogonal…
Diffractive systems are quantum-mechanical models with point-like singularities where usual semiclassical approximation breaks down. An overview of recent investigations of such systems is presented. The following examples are considered in…
This paper reports the results of extensive numerical studies related to spectral properties of the Laplacian and the scattering matrix for planar domains (called billiards). There is a close connection between eigenvalues of the billiard…
We revisit the spectral statistics of the C$_3$--symmetric billiard introduced by Dembowski [Phys. Rev. E, R4516 (2000)], which exhibits both GOE and GUE statistics depending on the symmetry block. Using high--precision Beyn's…
We study the convergence towards the equilibrium for a dissipative and stochastic time-dependent oval billiard. The dynamics of the system is described by using a generic four dimensional nonlinear map for the variables: the angular…
We study properties of a random walk in a generalized Sinai model, in which a quenched random potential is a trajectory of a fractional Brownian motion with arbitrary Hurst parameter H, 0< H <1, so that the random force field displays…
We study the gambler's ruin problem for a biased random walk on $\{0,1,\dots,a\}$ under multi-site geometric resetting: at each time step, the walker is reset with probability $\gamma\in(0,1)$ to a random position drawn from a distribution…
The phenomenon of quantum localization in classically chaotic eigenstates is one of the main issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or even in general wave mechanics. In this…
We study some statistical properties for the behavior of the average squared velocity -- hence the temperature -- for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the…
We compute single-particle energy spectra for a one-body hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of…
We present a functional analytic framework based on the spectrum of the transfer operator to study billiard maps associated with perturbations of the periodic Lorentz gas. We show that recently constructed Banach spaces for the billiard map…
The universal statistics of density fluctuations of localized quantum states may offer unprecedented opportunities to probe and understand quantum transport in connection with dimensionality, coherence, symmetry and disorder. To date, the…
We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain ${\mathcal D} \subset {\mathbb R}^d$ until it hits the boundary and bounces randomly inside according to some reflection…
We propose indicators of the discriminant for systems with generalized inversion symmetry which are computed from data only at high-symmetry points in the Brillouin zone. Our approach captures the exceptional points and their…
The Robnik billiard is investigated in detail both classically and quantally in the transition range from integrable to almost chaotic system. We find out that a remarkable correspondence between characteristic features of classical…
In this work we study the nonlinear dynamics of the static and the driven ellipse. In the static case, we find numerically an asymptotical algebraic decay for the escape of an ensemble of non-interacting particles through a small hole due…