An accelerator mode based technique for studying quantum chaos

We experimentally demonstrate a method for selecting small regions of phase space for kicked rotor quantum chaos experiments with cold atoms. Our technique uses quantum accelerator modes to selectively accelerate atomic wavepackets with localized spatial and momentum distributions. The potential used to create the accelerator mode and subsequently realize the kicked rotor system is formed by a set of off-resonant standing wave light pulses. We also propose a method for testing whether a selected region of phase space exhibits chaotic or regular behavior using a Ramsey type separated field experiment.Comment: 5 pages, 3 figures, some modest revisions to previous version (esp. to the figures) to aid clarity; accepted for publication in Physical Review A (due out on January 1st 2003

Global Diffusion in a Realistic Three-Dimensional Time-Dependent Nonturbulent Fluid Flow

We introduce and study the first model of an experimentally realizable three-dimensional time-dependent nonturbulent fluid flow to display the phenomenon of global diffusion of passive-scalar particles at arbitrarily small values of the nonintegrable perturbation. This type of chaotic advection, termed {\it resonance-induced diffusion\/}, is generic for a large class of flows.Comment: 4 pages, uuencoded compressed postscript file, to appear in Phys. Rev. Lett. Also available on the WWW from http://formentor.uib.es/~julyan/, or on paper by reques

Orthogonality Catastrophe in Parametric Random Matrices

We study the orthogonality catastrophe due to a parametric change of the single-particle (mean field) Hamiltonian of an ergodic system. The Hamiltonian is modeled by a suitable random matrix ensemble. We show that the overlap between the original and the parametrically modified many-body ground states, $S$, taken as Slater determinants, decreases like $n^{-k x^2}$, where $n$ is the number of electrons in the systems, $k$ is a numerical constant of the order of one, and $x$ is the deformation measured in units of the typical distance between anticrossings. We show that the statistical fluctuations of $S$ are largely due to properties of the levels near the Fermi energy.Comment: 12 pages, 8 figure

E10 and a "small tension expansion" of M Theory

A formal ``small tension'' expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite dimensional coset space E10/K(E10) where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10(R). For the proof we make use of a novel decomposition of E10 into irreducible representations of its SL(10,R) subgroup. We explicitly show how to identify the first four rungs of the E10 coset fields with the values of geometric quantities constructed from D=11 supergravity fields and their spatial gradients taken at some comoving spatial point.Comment: 4 page

Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect

The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent $\eta$ and the spectral compressibility $\chi$ at the mobility edge, $\chi=\eta/2d$, is confirmed for the integer quantum Hall delocalization transition. Our calculations are performed within the framework of an unitary network-model and represent a new method to investigate spectral properties of disordered systems.Comment: 5 pages, RevTeX, 3 figures, Postscript, strongly revised version to be published in PR

Mesoscopic motion of atomic ions in magnetic fields

We introduce a semiclassical model for moving highly excited atomic ions in a magnetic field which allows us to describe the mixing of the Landau orbitals of the center of mass in terms of the electronic excitation and magnetic field. The extent of quantum energy flow in the ion is investigated and a crossover from localization to delocalization with increasing center of mass energy is detected. It turns out that our model of the moving ion in a magnetic field is closely connected to models for transport in disordered finite-size wires.Comment: 4 pages, 2 figures, subm. to Phys.Rev.A, Rap.Co

Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization

The explicit analytical expression for the distribution function of parametric derivatives of energy levels ("level velocities") with respect to a random change of scattering potential is derived for the chaotic quantum systems belonging to the quasi 1D universality class (quantum kicked rotator, "domino" billiard, disordered wire, etc.).Comment: 11 pages, REVTEX 3.

Renormalization group approach to energy level statistics at the integer quantum Hall transition

We extend the real-space renormalization group (RG) approach to the study of the energy level statistics at the integer quantum Hall (QH) transition. Previously it was demonstrated that the RG approach reproduces the critical distribution of the {\em power} transmission coefficients, i.e., two-terminal conductances, $P_{\text c}(G)$, with very high accuracy. The RG flow of $P(G)$ at energies away from the transition yielded the value of the critical exponent, $\nu$, that agreed with most accurate large-size lattice simulations. To obtain the information about the level statistics from the RG approach, we analyze the evolution of the distribution of {\em phases} of the {\em amplitude} transmission coefficient upon a step of the RG transformation. From the fixed point of this transformation we extract the critical level spacing distribution (LSD). This distribution is close, but distinctively different from the earlier large-scale simulations. We find that away from the transition the LSD crosses over towards the Poisson distribution. Studying the change of the LSD around the QH transition, we check that it indeed obeys scaling behavior. This enables us to use the alternative approach to extracting the critical exponent, based on the LSD, and to find $\nu=2.37\pm0.02$ very close to the value established in the literature. This provides additional evidence for the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization-delocalization transition.Comment: 10 pages, 11 figure

Energy diffusion in strongly driven quantum chaotic systems

The energy evolution of a quantum chaotic system under the perturbation that harmonically depends on time is studied for the case of large perturbation, in which the rate of transition calculated from the Fermi golden rule exceeds the frequency of perturbation. It is shown that the energy evolution retains its diffusive character, with the diffusion coefficient that is asymptotically proportional to the magnitude of perturbation and to the square root of the density of states. The results are supported by numerical calculation. They imply the absence of the quantum-classical correspondence for the energy diffusion and the energy absorption in the classical limit $\hbar \to 0$.Comment: 12 pages, 3 figures, RevTe

Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface. As an example, we compute the Melnikov function for a perturbation of a three-dimensional map that has a heteroclinic connection between a pair of invariant circles. The intersection curves of the manifolds are shown to undergo bifurcations in homologyComment: LaTex with 10 eps figure