Recently discovered connections between integrable evolution equations and the motion of curves are based on the following fact: The Serret-Frenet equations are equivalent to the Ablowitz-Kaup-Newell-Segur (AKNS) scattering problem at zero eigenvalue. This equivalence identifies those evolution equations, integrable or not, that can describe the motion of curves.

We consider a wavelet analysis of various time series for the Duffing oscillator, for which there is a potential maximum and a harmonic forcing term, and we focus on time series that return to the region of the potential maximum. When the dynamics is chaotic and the time series is highly nonstationary, there are many significant higher harmonics in a Fourier expansion and the usual Fourier analysis is problematic, especially for short total times. We show that the wavelet analysis is a robust tool that may be used to obtain qualitative information for highly nonstationary time series—specifically, that it may be used to detect a small-amplitude harmonic forcing term even when the dynamics is chaotic and even for short total times.

A particle that decays by the simplest interaction into two other particles is placed in a space-periodic external potential that acts only on the initial particle. For a strong potential, the decay rate is slowed drastically under most initial conditions. Comparing to the second-order perturbation treatment of a model where the decaying particle is imbedded in a medium of heavy, uncorrelated particles, noninteracting except for a potential interaction with the decaying particle, we find similar rate modifications. There exist possible applications in the supernova and early Universe environment, as well as possible laboratory demonstration of the effect, which bears some relationship to the ‘‘quantum Zeno’’ effect.

We propose and investigate a large class of models possessing resonance factorized S matrices. The associated Casimir energy describes a rich pattern of renormalization-group trajectories related to flows in the coset models based on the simply laced Lie algebras. From a simple resonance S matrix satisfying the ‘‘${\mathrm{\phi }}^3$ property’’ we predict new flows in nonunitary minimal models.

Our method uses topological properties of the large clusters in the single-cluster algorithm of Wolff for Monte Carlo simulations of spin systems. We have applied this method to the d=3 Ising model with film geometry near the special transition. As a test for the method we determined the bulk critical temperature and the critical indices in fair agreement with the results obtained by other methods. The new results refer to the critical surface coupling ${\mathit{J}}_{1\mathit{c}}$/J=1.5004(20) and the surface exponents, where φ=0.461(15) and ${\mathrm{\beta }}_{\mathit{i}}^{\mathit{m}}$=0.237(5).

We present a computational framework not based on the string hypothesis for the thermodynamics of statistical and quantum field theory models solvable by the Bethe ansatz. In the cases of XXZ Heisenberg chain and the sine-Gordon quantum field theory we derive a single nonlinear integral equation which determines the free energy (or ground-state scaling function). Our approach is very effective at high temperature, and correctly reproduces the low-temperature central charge and the analytic structure of the corrections.

We consider the problem of thermally activated potential barrier crossing in the presence of fluctuations of the barrier itself. For piecewise linear barrier switching between two values as a Markov process, exact and Monte Carlo results reveal a novel resonantlike phenomenon as a function of the barrier fluctuation rate. For very slow variations the average crossing time is the average of the times required to diffuse over each of the barriers separately; for very fast variations the mean crossing time is that required to cross the average barrier. At intermediate rates the crossing is strongly correlated with the potential variation and the escape rate exhibits a local maximum at a ‘‘resonant’’ fluctuation rate.

We introduce and analyze a class of nonlinear Langevin equations that describe electrical transport in systems with electric-field thresholds, such as charge-density-wave systems biased just above threshold. For sufficiently large nonlinearities, the models are argued to exhibit scale-invaraint phases wherein spatial and temporal correlations decay algebraically; in particular, current and voltage fluctuations show 1/${\mathit{f}}^{\mathrm{\alpha }}$ noise with universal exponents α. The values of physical parameters required for the experimental observation of these phases are estimated.

We have measured the Rydberg constant by frequency comparison of the three transitions 2${\mathit{S}}_{1/2\mathrm{-}}$8${\mathit{S}}_{1/2}$, 2${\mathit{S}}_{1/2\mathrm{-}}$8${\mathit{D}}_{3/2}$, and 2${\mathit{S}}_{1/2\mathrm{-}}$8${\mathit{D}}_{5/2}$ in hydrogen with the difference of two optical standards, the methane-stabilized He-Ne laser and the iodine-stabilized He-Ne laser. The frequency of the iodine-stabilized He-Ne laser has been remeasured. The new value for the Rydberg constant, ${\mathit{R}}_{\mathrm{\infty }}$=109 737.315 683 0(31) ${\mathrm{cm}}^{\mathrm{-}1}$, is currently the most precise available.

Shapiro, Shepard, and Wong [Phys. Rev. Lett. 62, 2377 (1989)] suggested that a scheme of multiple phase measurements, using quantum states with minimum ‘‘reciprocal peak likelihood,’’ could achieve a phase sensitivity scaling as 1/${\mathit{N}}_{\mathrm{tot}}^2$, where ${\mathit{N}}_{\mathrm{tot}}$ is the mean number of photons availavle for all measurements. We have simulated their scheme for as many as 240 measurements and have found optimum phase sensitivities for 3≤${\mathit{N}}_{\mathrm{tot}}$≤120. A power-law fit to the simulated data yields a phase sensitivity that scales as 1/${\mathit{N}}_{\mathrm{tot}}^{0.85\pm 0.01}$. We conclude that reciprocal peak likelihood is not a good measure of sensitivity.

The SU(n) quantum chains with inverse-square exchange exhibit a novel form of Yangian symmetry compatible with periodic boundary conditions, allowing states to be countable. We characterize the ‘‘supermultiplets’’ of the spectrum in terms of generalized ‘‘occupation numbers.’’ We embed the model in the k=1 SU(n) Kac-Moody algebra and obtain a new classification of the states of conformal field theory, adapted to particlelike elementary excitations obeying fractional statistics.

The behavior of a q-deformed Heisenberg-Weyl algebra nearby q=1 is investigated. We calculate the q-deformed symplectic structure and * product up to the first-order corrections by using the q-analog of the boson coherent state. Within this order, the Poisson bracket associated with the symplectic structure coincides with the one extracted from the * product and gives the phase space realization of the original operator commutation relations.

We have evaluated the density-density static response of a many-body system by calculating with the quantum Monte Carlo method the energy and density change caused by an external potential. Our results for the linear response function of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at zero pressure and temperature are in excellent agreement with the available experimental data. The results for the response function of 2D electrons also at zero temperature, obtained within the fixed-node approximation, constitute the most accurate information available to date for this system.

On simple cubic lattices, we compute the low-temperature expansion for the energy of the Ising model through 50 excited bonds in three dimensions and 44 excited bonds in four dimensions. We also give the magnetization through 42 excited bonds. Our method is a recursive enumeration of states with given energies on a set of finite lattices with generalized helical boundary conditions. A linear combination of such lattices cancels finite volume effects.

We note that the neutron spin must be treated as an intrinsically quantum variable when determining electromagnetically induced phase shifts in neutron interferometry by computing the otherwise-classical action over the classical orbit. We show that a putative acceleration of the neutron (γ/mc)E×(μ×B) recently suggested by Anandan, is essentially unobservable in such measurements over segments of the orbit where the electric and magnetic fields are constant (or vary slowly), within standard electroweak theory.

A forest-fire model is introduced which contains a lightning probability f. This leads to a self-organized critical state in the limit f→0 provided that the time scales of tree growth and burning down of forest clusters are separated. We derive scaling laws and calculate all critical exponents. The values of the critical exponents are confirmed by computer simulations. For a two-dimensional system, we show that the forest density in the critical state assumes its minimum possible value, i.e., that energy dissipation is maximum.

It is known that statistical properties of the energy levels for various billiards on a constant-negative-curvature surface do not follow the universal random-matrix predictions. We show that nongeneric behavior of the systems investigated so far originates from the special arithmetic nature of their tiling groups, which produces an exponentially large degeneracy of lengths of periodic orbits. A semiclassical study of the two-point correlation function shows that the spectral fluctuations are close to Poisson-like ones, typical of integrable systems.

We introduce and study a new class of random sequential adsorption models which we call the coordination models. These exhibit longer-range interactions than any local models studied to data and are intractable to any analytic techniques heretofore developed. We present computer simulation results and derive a simple mean-field theory which agrees closely with the simulations.

We propose an experimental realization of cryptographic-key-sharing scheme exploiting quantum correlations between pair photons. Our experimental setup consists of an external source of correlated photon pairs which propagate to two widely separated unbalanced Mach-Zehnder interferometers. The probability of detection of photon pairs in any two outputs of the interferometers can be fully modulated by phase plates in either interferometer.

The complete sequence of 1060 eigenmodes with frequencies between 0.75 and 17.5 GHz of a quasi-two-dimensional superconducting microwave resonator shaped like a quarter of a stadium billiard with a Q value of Q≊${10}^{5–}$${10}^7$ was measured for the first time. The semiclassical analysis is in good agreement with the experimental data, and provides a new scheme for the statistical analysis and comparison with predictions based on the Gaussian orthogonal ensemble.