Related papers: Chaotic eigenfunctions in phase space
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
We consider the quantized hyperbolic automorphisms on the 2-dimensional torus (or generalized quantum cat maps), and study the localization properties of their eigenstates in phase space, in the semiclassical limit. We prove that if the…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
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.…
For chaotic scattering systems we investigate the left-right Husimi representation, which combines left and right resonance states. We demonstrate that the left-right Husimi representation is invariant in the semiclassical limit under the…
We present a novel extension of the concept of scars for the wave functions of classically chaotic few-body systems of identical particles with rotation and permutation symmetry. Generically there exist manifolds in classical phase space…
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…
New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point…
We investigate the quantum properties of a non-random Hamiltonian with a step-like singularity. It is shown that the eigenfunctions are multifractals and, in a certain range of parameters, the level statistics is described exactly by…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
A two-step optimization is proposed to represent an arbitrary quantum state to a desired accuracy with the least number of gaussians in phase space. The Husimi distribution of the quantum state provides the information to determine the…
One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds have different dimensions. In this paper, in trying to…
We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…
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…
We investigate the emergence of chaotic dynamics in a quantum Fermi - Pasta - Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization…
The eigenmode spectrum is a fundamental starting point for the analysis of plasma stability and the onset of turbulence, but the characterization of the spectrum even for the simplest plasma model, ideal magnetohydrodynamics (MHD), is not…
Some non-Gaussian aspects of chaotic transport are investigated for a general class of two-dimensional area-preserving maps. Kurtosis, in particular, is calculated from the diffusion and the Burnett coefficients, which are obtained…
We consider deterministic chaotic models of vacuum fluctuations on a small (quantum gravity) scale. As a suitable small-scale dynamics, nonlinear versions of strings, so-called `chaotic strings' are introduced. These can be used to provide…
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…
We study the universal structure of late-time ensembles obtained from unitary dynamics in quantum chaotic systems with symmetries, such as charge or energy conservation. We find that although quantum states do not ergodically explore the…