A simple theory is developed for rough seas in which the energy cascade towards small scales is too much for a surface tension dominated wrinkling of the surface to handle. We suggest that a new phase, consisting of an air-water foam, is created and becomes the principal medium for energy dissipation. The foam depth and droplet size are calculated and we suggest how the predicted dependence on energy flux and surface tension could be verified experimentally.

I propose a numerical simulation algorithm for statistical systems which combines a microcanonical transfer of energy with global changes in clusters of spins. The advantages of the cluster approach near a critical point augment the speed increases associated with multispin coding in the microcanonical approach. The method also provides a limited ability to tune the average cluster size.

It is shown that the recent Greenberger-Horne-Zeilinger ‘‘all or nothing’’ contradiction of quantum mechanics with local realism can be exhibited on a macroscopic scale where a large number of particles are incident on each analyzer. We present a formulation of the all or nothing paradox in terms of boson fields, and suggest how the paradox might be realized using a correlated photon triplet. The suggested experiment might be readily extended to test, for the first time to our knowledge, quantum mechanics against local realism for situations of more than one quanta per wave packet incident on each measurement apparatus.

A geometrical phase is constructed for dissipative dynamical systems possessing continuous symmetries. It emerges as the natural analog of the holonomy associated with the adiabatic variation of parameters in quantum-mechanical and classical Hamiltonian systems. In continuous media, the physical manifestation of this phase is a spatial shift of a wave pattern, typically a translation or rotation. An illustration associated with pattern formation in fluids is provided.

We prove that the temporal autocorrelation function C(t) for quantum systems with Cantor spectra has an algebraic decay C(t)∼${\mathit{t}}^{\mathrm{-}\mathrm{\delta }}$, where δ equals the generalized dimension ${\mathit{D}}_2$ of the spectral measure and is bounded by the Hausdorff dimension ${\mathit{D}}_0$≥δ. We study various incommensurate systems with singular continuous and absolutely continuous Cantor spectra and find extremely slow correlation decays in singular continuous cases (δ=0.14 for the critical Harper model and 0<δ≤0.84 for the Fibonacci chains). In the kicked Harper model we deomonstrate that the quantum mechanical decay is unrelated to the existence of classical chaos.

The rotation of the reference frame of a particle is known to lead to a phase change of its wave function proportional to its angular momentum. This can manifest itself as an angle-dependent phase shift of a photon scattered by a fixed target, when the photon state is an eigenstate of the component of total angular momentum perpendicular to the scattering plane. This phase shift has been observed in the quantum beat pattern resulting from the transient excitation of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ nuclei by synchrotron radiation.

We formulate one-dimensional many-body integrable systems in terms of a new set of phase space variables involving exchange operators. The Hamiltonian in these variables assumes a decoupled form. This greatly simplifies the derivation of the conserved charges and the proof of their commutativity at the quantum level.

An analytic expression is derived for the Lyapunov exponents of the product of random transfer matrices related to the Ising model with quenched disorder in one dimension. We find a deterministic map which transforms the original system to a new one with zero external field and constant coupling. The free energy and the rate of correlation decay are thus obtained in terms of an exponentially convergent series. Our results can be generalized to the product of random matrices with nonzero entries.

In this Letter we report a new construction to obtain restricted solid-on-solid (RSOS) models out of loop models. The method is a generalization of ideas developed by Owczarek and Baxter, and by Pasquier. In particular we consider a solvable O(n) model and point out that some of the RSOS models thus obtained admit an off-critical extension. Among these models we find a spin-1 Ising model, which is solvable not only at the critical point, but also in a fieldlike deviation away from it. We calculate the critical exponent δ=15 directly from the relation between the free energy and the field. This is the first determination of this exponent without the use of scaling relations.

Integrable systems related to the Korteweg–de Vries (KdV) equation are shown to be associated with the dynamics of vortex patches in ideal two-dimensional fluids. This connection is based on a truncation of the exact contour dynamics analogous to the ‘‘localized induction approximation’’ which relates the nonlinear Schrödinger equation to the motion of a vortex filament. Single soliton solutions of the periodic modified KdV problem correspond to uniformly rotating shapes which approximate the Kirchoff ellipse and known generalizations. A simple geometrical interpretation of the dual Poisson bracket structure of the modified KdV hierarchies is given.

In the linear regime close to equilibrium macroscopic transport coefficients can be calculated from the well-known Green-Kubo relations. Recently it has been shown, by Evans, Cohen, and Morriss that even far from equilibrium, bulk thermal transport coefficients can be calculated from the maximal, phase-space, Lyapunov exponents. In the present paper we point out that the Lyapunov exponents themselves can be expressed in terms of time correlation functions that are reminiscent of the Green-Kubo relations for Navier-Stokes transport coefficients.

A set of exactly solvable one-dimensional quantum-mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and Pöschl-Teller potentials. A general solution includes Shabat’s infinite number soliton system and leads to raising and lowering operators satisfying a q-deformed harmonic-oscillator algebra. In the latter case the energy spectrum is purely exponential and physical states form a reducible representation of the quantum conformal algebra ${\mathrm{su}}_{\mathit{q}}$(1,1).

The Van Vleck–Gutzwiller propagator is a fundamental quantity in semiclassical theory whose validity was recently demonstrated to extend beyond the time previously thought feasible, i.e., well past the time after which classical chaos has mixed the phase space on a scale smaller than Plancks’s constant. Little justification was given for this seeming contradiction of the usual vision of semiclassical errors. Though perhaps nonintuitive, we find that standard arguments, properly applied to chaotic dynamics, do explain the long time accuracy.

Using semiclassical arguments substantiated by numerical results for the quantum kicked rotor, we establish that breaking an antiunitary symmetry in a system with dynamical localization increases the localization length by a factor of 2. The transition between the symmetric and the symmetry broken case is smooth. The semiclassical theory provides an approximate expression for the transition function as well as the critical strength of the symmetry-breaking interaction necessary to achieve the full factor of 2 increase of the localization length.

We describe the results of studies of a random-anisotropy Blume-Emery-Griffiths spin-1 Ising model using mean-field theory, transfer-matrix calculations, and position-space renormalization-group calculations. The interplay between the quenched randomness of the anisotropy and the annealed disorder introduced bythe spin-1 model leads to a rich phase diagram with a variety of phase transitions and reentrant behavior. Our results may be relevant to the study of the phase separation of ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He mixtures in porous media in the vicinity of the superfluid transition.

The bubble picture for pair-spin correlation functions is applied to two-dimensional Ising-like models, at subcritical temperatures, in an external field h, from which we show, via the fluctuation sum, that the susceptibility χ(h) has an essential singularity at h=0. This is studied further using a solid-on-solid bubble model for (a) a restricted ensemble corresponding to metastability, where h=0 is found to be the limit point of an infinite number of poles of χ along the negative real axis, and (b) an unrestricted ensemble, where a Yang-Lee circle theorem is found.

We show that the low-lying spectrum of three noninteracting anyons in a harmonic potential can be qualitatively and quantitatively understood on the basis of a simple set of analytic wave functions. These wave functions are exact in both the boson and fermion limits and satisfy the anyone wave-function phase condition at all intermediate values of the statistical parameter 0<α<1. The resulting nonlinear spectrum agrees with those of exact numerical calculations to better than a few parts in a thousand.

Damage spreading in the nearest-neighbor Ising model on a triangular lattice, for ferro- and antiferromagnetic interactions, is investigated using Glauber dynamics. Two procedures for updating spins are employed, the sequential and parallel ones. (a) The sequential algorithm leads to a dynamic transition at a temperature very close to the usual static critical temperature ${\mathit{T}}_{\mathit{c}}$ in the ferromagnetic case, whereas in the antiferromagnetic problem, no transition is found, suggesting that the equilibrium phase transition and the frozen-chaotic one are strongly correlated. (b) The parallel recipe is not able to distinguish the two interactions, giving a similar dynamic transition for both, at a temperature which is considerably different from the ferromagnetic Curie temperature.

We consider the motion of a classical particle in (1+1)-dimensional space-time. Four probability distributions govern the trajectory of the particle; these give the probability of moving to the left or right in space while moving backwards or forwards in time. If these probabilities are randomly distributed and if the probability of moving backwards in time is related to the probability of moving forwards in time in a prescribed manner, then the master equations for these probabilities give rise to the Dirac equation without recourse to direct analytic continuation. In contrast, when a particle always moves forward in time, an analytic continuation is required to recover the Dirac equation.

Asymptotic formulas for the probability of finding exactly n eigenvalues in an interval of length s, for large s and fixed n, are given for random matrices taken from the Gaussian ensembles (β=1,2,4). These exact results are compared with the predictions of a continuum Coulomb gas model due to Dyson.