Related papers: Statistical properties of high-lying chaotic eigen…
Generic low-dimensional Hamiltonian systems feature a structured, mixed classical phase-space. The traditional Percival classification of quantum spectra into regular states supported by quasi-integrable regions and irregular states…
Quantum walks are at present an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior.…
We studied the statistical properties of a quantum system in the pseudo-integrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like…
For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between "perturbative" and "non-perturbative" regimes,…
Wavefunctions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wavefunctions display universal density distributions and density auto-correlations in agreement with…
We study chaotic eigenfunctions in wedge-shaped and rectangular regions using a generalization of Berry's conjecture. An expression for the two-point correlation function is derived and verified numerically.
We describe the statistics of chaotic wavefunctions near periodic orbits using a basis of states which optimise the effect of scarring. These states reflect the underlying structure of stable and unstable manifolds in phase space and…
The impression gained from the literature published to date is that the spectrum of the stadium billiard can be adequately described, semiclassically, by the Gutzwiller periodic orbit trace formula together with a modified treatment of the…
Classical chaotic systems with symbolic dynamics but strong pruning present a particular challenge for the application of semiclassical quantization methods. In the present study we show that the technique of periodic orbit quantization by…
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…
Numerical calculations studying bound eigenstates in chaotic regions of phase space, including those of the stadium billiard, are summarized. These calculations demonstrate that the scars of periodic orbit model is seriously flawed. An…
Our current understanding of quantum chaos in many-body quantum systems hinges on the random matrix theory(RMT) behavior of eigenstates and their energy level statistics. Although RMT has been remarkably successful in describing `coarse'…
Dynamical billiards, or the behavior of a particle traveling in a planar region $D$ undergoing elastic collisions with the boundary, has been extensively studied and is used to model many physical phenomena such as a Boltzmann gas. Of…
The geometry of a billiard boundary fundamentally governs its dynamics, ranging from integrable to mixed and fully chaotic regimes. Bean- and peanut-shaped billiards have varying curvature with both focusing and defocusing walls without a…
Periodic orbit theory for classical hyperbolic system is very significant matter of how we can interpret spectral statistics in terms of semiclassical theory. Although pruning is significant and generic property for almost all hyperbolic…
By using the Krylov subspace technique to generate the spin coherent states in kicked top model, a prototype model for studying quantum chaos, the accessible system size for studying the Husimi functions of eigenstates can be much larger…
We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation…
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear $\sigma$-model…
We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision…
We investigate the statistics of eigenstates in a weak self-affine disordered potential in one dimension, whose Gaussian fluctuations grow with distance with a positive Hurst exponent $H$. Typical eigenstates are superlocalized on samples…