The kicked rotator on a torus is a system with a bounded phase space in which a chaotic diffusion occurs for a large enough perturbation strength. The quantum version of this model exhibits localization effects which produce deviations from random-matrix-theory predictions. We show that these localization effects display a scaling behavior which is a counterpart of the scaling theory of one-dimensional Anderson localization in finite samples. We suggest that this behavior can be highly relevant to some general problems of quantum chaos.

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. These ‘‘scarred’’ wave functions provide a new basis for the quantum description of variety of classically chaotic systems.

We performed light-scattering experiments on a mixture of hydrogen and argon. By varying the density of the sample, we can probe the range of reduced wave vectors in which Campa and Cohen [Phys. Rev. A 39, 4909 (1989)] predicted, in dilute disparate-mass gas mixtures, the onset of a mode supported by the light particles: the fast sound mode. The presence of the additional sound mode can be established most conveniently by analyzing ${\omega }^2$I(k,ω) rather than I(k,ω). Our results for the shift of fast and slow sound match the theoretical predictions very well.

We study the surface and the reflection cluster algorithms, which have been developed for systems with global continuous symmetries by Niedermayer and Wolff, respectively, in the O(4) spin model in four dimensions. The surface algorithm appears not to be substantially better than local algorithms for this model. We show that the reflection algorithm has big advantages: It fights critical slowing down and due to the use of improved estimators it gives a variance reduction.

We study the quantization of the coset space SU(3)/U(1)×U(1), considered as an example of a compact phase space. We embed this system in the flat space $C^6$ endowed with a Poisson-bracket structure, then quantize it as a constrained system, finding consistency only for isolated symplectic structures. The space of states for each admissible symplectic structure forms an irreducible representation of SU(3). In this way, we recover in the language of constrained dynamics some of the results of the Borel-Weil-Bott theorem and geometric quantization.

We consider the 3D Schrödinger equation with a potential having no spherical symmetry and show that such a potential can be constructed from the scattering operator by using the solution of a Fredholm integral equation. The Fredholm integral operator presented is compact and self-adjoint; its eigenvalues are symmetric about 0 and lie in [-1,1].

We show that the Aharonov-Bohm effect requires that the vector potential couple minimally to matter, not that it be a gauge field: The effect is present in massive (finite-range) electrodynamics, reducing smoothly to the original result in the limit of infinite range. Indeed, it may be used to provide an experimental bound on the range which is much larger than the ‘‘table-top’’ apparatus, namely a lower limit of order ${10}^2$ km.

We consider in this note the time dependence of a system for which two levels (which are not in general decoupled) accidentally cross (or almost cross) for some value of the parameters of the Hamiltonian. We show that for a well-defined class of crossings or narrowly avoided crossings, in which the Hamiltonian changes slowly on its own scale, the system will behave oppositely to the usual adiabatic rule.

In this paper the crossover from ‘‘small’’ to ‘‘large’’ chaotic systems is studied. The behavior of the largest Lyapunov exponent in a system of coupled chaotic maps shows that this crossover is remarkably sharp, and allows us to define a coherence length beyond which the system is effectively large. Between the coherent chaos of the small system and the incoherent chaos (turbulence) of the large one there is a stable window starting at the linear instability point for the uniform chaotic state in which the lattice becomes effectively one dimensional. The scaling of the coherence length close to the onset of turbulence is investigated and compared to recent predictions.

We compute the velocity autocorrelation function of a tagged particle in a two-dimensional lattice-gas cellular automaton using a method that is about a million times more efficient than existing techniques. A ${\mathrm{t}}^{\mathrm{-}1}$ algebraic tail in the tagged-particle velocity autocorrelation function is clearly observed. The amplitude of this tail is predicted to within a few percent by a lattice-gas version of mode-coupling theory. The magnitude of logarithmic corrections to the ${\mathrm{t}}^{\mathrm{-}1}$ tail is much smaller than expected for continuous fluids.

The dielelctric breakdown model (DBM) is generalized to include lower cutoffs, which prevent growth at low fields. The new models may represent realistic situations in some DBM and some viscous fingering experiments. Multifractal theory is shown to provide quantitative predictions for the crossover from the usual DBM patterns (at small finger sizes) to a new, spiky, behavior (at large sizes). For one of the models, the theory also predicts when growth will stop. The predicted crossover scaling function is confirmed by numerical simulations.

We numerically study the quantized verion of the Frenkel-Kontorova model, using Feynman quantization and the Metropolis algorithm. The gross structure of the quantum ground state above the critical parameter value mirrors the classical equilibrium configuration, provided that ħ is not too large; nevertheless, its fine structure is significantly different, and can be related to a sawtooth map rather than to the standard map. The dependence of energy on temperature is also investigated and is explained in terms of the quantum phonon spectrum for linearized motion.

We have studied the behavior of the Floquet spectrum for A Fokker-Planck equation describing a nonlinear Brownian rotor driven by an angle-dependent dynamic external force consisting of two traveling sine waves with amplitudes ${\epsilon }_1$ and ${\epsilon }_2$. For the case ${\epsilon }_2$=0, the Fokker-Planck equation is separable (in the sense that is has two well defined eigen-numbers) and the nearest-neighbor spacing distribution appears to be Poisson random for small spacings. For both ${\epsilon }_1$≠0 and ${\epsilon }_2$≠0, we observed nonlinear resonance and level repulsion, indicating that the spectrum, at least locally, exhibits universal random-matrix-type behavior and that information about the underlying dynamics of the Brownian particle is lost from the spectrum.

Irregularity of the eigenvalue sequence in a quantum nonintegrable system is investigated from the viewpoint of algorithmic complexity theory. An example of a real symmetric matrix whose eigenvalue sequence has null complexity but whose nearest-neighbor level spacing shows the Wigner-type distribution is presented. Numerical examinations demonstrate that the algorithmic complexity of eigenvalues of a nonintegrable Hamiltonian system also turns out to be null.

We define fractal shot noise, which is a stationary continuous-time process that is fundamentally different from fractional Brownian motion. Two applications in physics are considered: the mass distribution of collections of solid-particle aggregates and the electric field at the growing edge of a doped semiconductor quantum wire. For a broad range of parameters, the amplitude probability density function of this process is a Lévy-stable random variable with dimension less than unity; it therefore does not converge to Gaussian form.

Ising models with correlated or uncorrelated random horizontal bonds are studied for square lattices in zero field. The partition sum is expressed in terms of a one-component field. Griffiths singularities in the free energy as function of temperature are derived. They are log-transforms of certain Lifshitz band tails. Griffiths singularities occur above as well as below the critical temperature.

We define a variant of the model of Bak, Tang, and Wiesenfeld of self-organized critial behavior by introducing a preferred direction. We characterize the critical state and, by establishing equivalence to a voter model, determine the critical exponents exactly in arbitrary dimension d. The upper critical dimension for this model is three. In two dimensions the model is equivalent to an earlier solved special case of directed percolation.

We have performed a test of Lorentz invariance by searching for a time-dependent quadrupole splitting of Zeeman levels in ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$. A component of the splitting at a twice the Earth’s sidereal frequency (${\mathrm{\Omega }}_{\mathrm{S}}$) would suggest a preferred direction which affects the local physics of the ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ nucleus. The technique employs polarized ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ gases produced by spin exchange with laser optically pumped Rb. Both species are contained in the same glass cell, the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ providing magnetometry and a monitor of systematic effects. Data from two runs produce an upper limit at the 1σ confidence level of 2×${10}^{\mathrm{-}21}$ eV (0.45×${10}^{\mathrm{-}6}$ Hz) on the Lorentz-invariance violating contribution to the binding energy. This result is comparable to that of the most precise previous experiment.

We investigate some two- and three-dimensional Ising models with multispin interactions and a field, by means of Monte Carlo simulations. The phase diagram of these models contains a self-dual line, along which we have searched for the presence of a phase transition. Both in two and three dimensions we give examples exhibiting a first-order transition along a part of the self-dual line. These first-order lines end in critical points, which are classified as Ising-type in terms of universality. A lattice-gas interpretation of these models clearly shows their similarity with gas-liquid systems.

We solve an initial-boundary value problem for the Davey-Stewartson equation, a multidimensional analog of the nonlinear Schrödinger equation. It is shown that for large time, an arbitrary initial disturbance will, in general, decompose into a number of two-dimensional coherent structures. These structures exhibit interesting novel features not found in one-dimensional solitons.