Hamiltonian systems describing particle motion in a wave with time-dependent (chirped) frequency are studied. The wave is found to form a single-node separatrix (bucket) moving in the phase space at a rate proportional to that of the frequency change. Particles trapped inside the bucket undergo convection, while untrapped particles colliding with the bucket get a resonant kick, in phase space. In toroidal systems, these effects can result in a large radial convective flux roughly proportional to the size of the bucket and the frequency chirping. Possible applications of this novel mechanism to tokamak plasmas are discussed.

Quantum wave function of a chaotic system spreads rapidly over distances on which the potential is significantly nonlinear. As a result, the effective force is no longer just a gradient of the potential, and predictions of classical and quantum dynamics begin to differ. We show how the interaction with the environment limits distances over which quantum coherence can persist, and therefore reconciles quantum dynamics with classical Hamiltonian chaos. The entropy production rate for such open chaotic systems exhibits a sharp transition between reversible and dissipative regimes, where it is set by the chaotic dynamics.

An ideal grey body is a macroscopic object with definite temperature which absorbs only a fraction of the radiation incident on it. Assuming that a grey body always emits in a mixed state, and that the radiation density matrix factors into matrices for the various frequency modes, we employ general arguments to derive the complete statistic of grey-body radiance elicited by incident radiation. These depend only on the temperature and the absorptivities for the various frequencies (hence are of universal form), and coincide with the statistics of black-hole radiance first derived a decade and a half ago.

We show the existence of a nonadiabatic geometric phase, i.e., an Aharonov-Anandan (AA) phase, in the Aharonov-Casher (AC) topological interference effect in one-dimensional mesoscopic rings. We find the AC phase is the phase accumulated by the spin wave function during a cyclic evolution, and show it is the sum of a geometric AA phase and a dynamical phase. In the adiabatic limit, the AA phase becomes the spin-orbit Berry phase introduced by Aronov and Lyanda-Geller. By solving exactly the model of a quasi-one-dimensional ring formed by the 2DEG on a semiconductor heterostructure, we discuss the observability of the AA phase in the AC effect.

We show that in a parameter range which is important in particular for optical instabilities spiral waves in the complex (generalized) Ginzburg-Landau equation are unstable with respect to a core instability which leads to spontaneous acceleration of the spiral. Depending on the parameters the system settles down in at least four qualitatively different spatiotemporally chaotic states.

An optimization problem that may be cast in the context of domain walls in ferromagnets and spin glasses, latice animals, and percolation is described. Numerical calculations in two and three dimensions show that a new universality class is obtained. In the strong disorder limit interfaces are not self-affine but fractal. Further, the nontrivial ground state of frustrated spin glasses is straightforwardly obtained in this limit.

We describe a new realization of stochastic resonance, applicable to a broad class of systems, based on an underlying excitable dynamics with deterministic reinjection. A simple but general theory of such ‘‘single-trigger’’ systems is compared with analog simulations of the Fitzhugh-Nagumo model, as well as experimental data obtained from stimulated sensory neurons in the crayfish.

The general 1D double-well model with anharmonic interaction is considered in the displacive limit. Expansion of the Hamiltonian around a multikink state results in a phonon-kink Hamiltonian. It is shown that at rather low temperatures and short wave lengths the phonon-kink interaction can be treated in Born approximation, leading to a decomposition of the multikink-phonon Hamiltionian. Elimination of the phonons results in an effective potential for the kink-kink interaction, which corresponds to the one-dimensional analog of the RKKY interaction. This long-range interaction is inherent only for models with anharmonic on-site potentials and not in case of a double-parabola model.

We demonstrate that stochastic resonance, where an increase in the noise acting on a nonlinear dynamical system increases the signal-to-noise ratio describing the response to periodic driving, can occur in quantum systems as well as classical ones. We show that quantum stochastic resonance can be observed experimentally by measuring conductance fluctuations in mesoscopic metals and describe the experimental parameters for which it occurs.

We provide a streamlined proof of Hardy’s theorem, that almost every entangled state for a pair of quantum particles admits a ‘‘proof of nonlocality’’ without inequalities. Moreover, our analysis covers a larger class of observables. Thus we also strengthen Hardy’s assertion that the argument fails for maximally entangled states, such as the singlet state. At the same time, we formulate the argument in such a manner that the relations which must be satisfied for local hidden variables are entirely deterministic, making no reference whatsoever to probability, let alone probablistic inequalities.

We present a measurement setup based on the deflection of atoms from a quantized electromagnetic field and a strategy which leads to the knowledge of the complete quantum state of this field. The same setup reveals the expectation value of the phase operator $e^{i\phi }$.

We analyze the effect of internal degrees of freedom on the movability properties of localized excitations on nonlinear Hamiltonian lattices by means of properties of a local phase space which is at least of dimension six. We formulate generic properties of a movability separatrix in this local phase space. We prove that due to the presence of internal degrees of freedom of the localized excitation it is generically impossible to define a Peierls-Nabarro potential in order to describe the motion of the excitation through the lattice. The results are verified analytically and numerically for Fermi-Pasta-Ulam chains.

We propose a new nonrelativistic Chern-Simons theory based on a simple modification of the standard Lagrangian. This admits asymptotically nonvanishing field configurations and is applicable to the description of systems of repulsive bosons. The new model supports topological vortices and has a self-dual limit, both in the pure Chern-Simons and in the mixed Chern-Simons-Maxwell cases. The analysis is based on a new formulation of the Chern-Simons theories as constrained Hamiltonian systems.

The mean area of two-dimensional unpressurized vesicles, or self-avoiding loops of fixed length N, behaves for large N as ${\mathit{A}}_0$${\mathit{N}}^{3/2}$, while their mean square radius of gyration behaves as ${\mathit{R}}_0^2$${\mathit{N}}^{3/2}$. The amplitude ratio ${\mathit{A}}_0$/${\mathit{R}}_0^2$ is computed exactly and found to equal 4π/5. The physics of the pressurized case, in both the inflated and collapsed phases, may be usefully related to that of a complex O(n) field theory coupled to a U(1) gauge field, in the limit n→0.

We bosonize the low energy excitations of Fermi liquids in any number of dimensions in the limit of long wavelengths. The bosons are a coherent superposition of electron-hole pairs and are related with the displacements of the Fermi surface in some arbitrary direction. A coherent-state path integral for the bosonized theory is derived and it is shown to represent histories of the shape of the Fermi surface. The Landau theory of Fermi liquids can be obtained from the formalism in the absence of nesting of the Fermi surface and singular interactions. We show that the Landau equation for sound waves is exact in the semiclassical approximation for the bosons.

A formalism is developed for studying genetic algorithms by considering the evolution of the distribution of fitness in the population. The effects of selection on the population are problem independent. The formalism predicts the optimal amount of selection. Crossover is solved for a model problem-finding low energy states of the one dimensional Ising spin glass. The theory is found to be in good agreement with simulations.

Time-independent wave-packet forms of the Schrödinger equation (TIWSE) and Lippmann-Schwinger equation (TIWLSB) have been derived by a partial time-to-energy Fourier transform of ${\mathit{L}}^2$ wave-packet solutions to the time-dependent Schrödinger equation. The new equations retain the initial wave packet χ(${\mathit{t}}_0$) as a ‘‘universal source’’ of scattered waves, which applies for all collision energies E contained in the initial wave packet. The relationship between the solution ${\mathrm{\Psi }}_{\mathit{t}0}$(E) of the TIWSE or TIWLSE and the scattering solution ${\mathrm{\Psi }}^{\mathrm{}(+)\mathrm{}}$(E) of the standard time-independent Lippmann-Schwinger or Schrödinger equation is given and the method illustrated by a computational application.

A method is proposed for the experimental determination of the amplitude and phase structure of a quasimonochromatic wave field in a plane normal to its propagation direction. The wave field may represent either a scalar electromagnetic (EM) field or the quantum mechanical (QM) wave function of a matter wave. For coherent EM fields or pure QM states, the method uniquely reconstructs the complex wave fields. For partially coherent EM fields or mixed QM states, it reconstructs the two-point correlation function or density matrix. The experiment uses only intensity measurements and refractive optics (lenses), and the data analysis algorithm is noniterative and requires no deconvolution.

We propose a classical model for the non-Abelian Chern-Simons theory coupled to N pointlike sources and quantize the system using the Becchi-Rouet-Stora-Tyutin technique. The resulting quantum mechanics provides a unified framework for fractional spin, braid statistics, and Knizhnik-Zamolodchikov equation.

We outline a procedure whereby higher-order corrections to the semiclassical propagator can be systematically computed within classical mechanics. The application of this result to actual calculations is straightforward.