We apply a generalized transfer-matrix method to the d=2 Ising ferromagnet at H≠0 and T<${\mathit{T}}_{\mathit{c}}$ to obtain complex constrained free energies. Although the method does not explicitly introduce droplets, the imaginary parts of those constrained free energies that correspond to the metastable state are accurately predicted by a field-theoretical droplet model. The free energy of a critical droplet is given by an equilibrium Wulff construction, and we find evidence for Goldstone modes on its surface. These results indicate that our approach provides a nonperturbative numerical continuation of the free energy around the essential singularity at H=0.

We present the analytic solution of the self-organized critical (SOC) forest-fire model in one dimension proving SOC in systems without conservation laws by analytic means. Under the condition that the system is in the steady state and very close to the critical point, we calculate the probability that a string of n neighboring sites is occupied by a given configuration of trees. The critical exponent describing the size distribution of forest clusters is exactly τ=2 and does not change under certain changes of the model rules. Computer simulations confirm the analytic results.

It is shown that when a quantum mechanical oscillator is parametrically excited there are special values of the parameters for which the system will pass periodically through a lattice of coherent states associated with the modular group Γ. It is shown that these Γ transits can be used to determine unknown parameters. A method is given for detecting the transits experimentally and is made possible by the existence of three families of states associated with modular forms that are orthogonal to the lattice. For isotropic states the three families occur in D-mode systems with D>10, 14, and 26.

A generalization of the Jordan-Wigner transformation to three (or higher) dimensions is constructed. The nonlocal mapping of spin to fermionic variables is expressed as a gauge transformation with topological charge equal to 1. The resulting fermionic theory is minimally coupled to a non-Abelian gauge field in a spontaneously broken phase containing monopoles.

The crossing processes in an overdamped double-well potential driven by an external colored noise and a weak sinusoidal time-dependent modulation are investigated by means of analog simulation. A new resonance is revealed (besides the so-called stochastic resonance) for frequencies close to the inverse time constant of the colored intrawell dynamics (resonant crossing). A quantitative analysis of the results obtained is also proposed.

Temporal Bell inequalities can be violated for sequences of events (histories) for which probabilities satisfying consistent sum rules cannot be defined. We discuss possible experiments in which such violations, never observed so far, may indeed be seen. The basic scheme, which uses three optically driven and mutually interacting two-level systems, could be implemented in a variety of nanostructures. It could even be mapped onto the dynamics of a single electron four-level system thus allowing for a realization in atomic physics.

We consider generalized commutation relations in a dynamically evolving curved spacetime which, prior to some initial time and subsequent to some later time, is flat. By considering the Bogoliubov transformations associated with gravitationally induced particle creation, we find that the consistent evolution of the generalized commutation relations from the first flat region to the second flat region can only occur if q=±1.

We give a wide class of Lie-Poisson systems for which explicit, Lie-Poisson integrators, preserving all Casimirs, can be constructed. The integrators are extremely simple and have widespread applicability. Examples are the free rigid body, a moment truncation, and a new, fast algorithm for the sine-bracket truncation of the 2D Euler equations.

The number of levels with energy less than E of an integrable quantum system with two degrees of freedom is equal to λE+${\mathit{sE}}^{1/4}$, where λ is a constant and s a fluctuating quantity with a non-Gaussian distribution. The probability distribution of s decreases roughly like exp(-${\mathit{s}}^4$) when s is large. The number of levels between E and E+z √E is equal to λz √E +${\mathit{rE}}^{1/4}$ where r is another fluctuating quantity. The distribution of r tends to a Gaussian distribution as z→0 and oscillates around some limiting non-Gaussian distribution as z→∞.

We propose a ladder-operator method for obtaining the squeezed states of general symmetry systems. It is a generalization of the annihilation-operator technique for obtaining the coherent states of symmetry systems. We connect this method with the minimum-uncertainty method for obtaining the squeezed and coherent states of general potential systems, and comment on the distinctions between these two methods and the displacement-order method.

The classical action for interacting strings, obtained by generalizing the time-symmetric electrodynamics of Wheeler and Feynman, is exactly additive. The additivity of the string action suggests a connection between the area of the string world sheets and entropy. We find that the action principle of classical mechanics is the condition that the total entropy of the strings be at an extremum, and the path-integral representation of the quantum density matrix element is an approximation to the partition function of the string theory.

The focusing nonlinear Schrödinger equation is numerically integrated over moderate to long time intervals. In certain parameter regimes small errors on the order of roundoff grow rapidly and saturate at values comparable to the main wave. Although the constants of motion are nearly preserved, a serious phase instability (chaos) develops in the numerical solutions. The instability is found to be associated with homoclinic structures and the underlying mechanisms apply equally well to many Hamiltonian wave systems.

The presence of a natural boundary in the angle complex plane of the function conjugating an area preserving map with a rotation is a signature of nonintegrability. Numerical results suggest that the boundary arises from the condensation of singularities when a real nonresonant frequency is approached by a sequence of complex resonant frequencies. For the quadratic map of the complex plane F: z’=λz+${\mathit{z}}^2$ the function conjugating the linear part of F with F has q cuts with end points on a spiral if λ=${\mathit{e}}^{2\mathrm{\pi }\mathit{i}\mathit{p}/\mathit{q}\mathrm{-}\mathrm{\alpha }}$ with α>0. When p/q tends to a (quadratic) irrational number and α→0 the points coalesce on the boundary of a circle, whose image is the Siegel disk.

We derive the form and properties of the generalization error for a self-similar feedforward network (constructed through an iterative procedure of test set partitioning combined with majority voting). We discuss the universality of these results and conjecture that the generalization error rate ε(α) as a function of the amount of training α never decreases faster than ε(α)-1/2∼ √α in the limit α→0. We show how the self-similar architecture can be used to improve the generalization performance.

A scheme to realize an optical switch with quantum coherence between its ‘‘open’’ and ‘‘closed’’ states is presented. It involves a single atom in a superposition of circular Rydberg states crossing a high Q cavity. A combination of switches could be used to prepare a quantum superposition of coherent microwave field states located simultaneously in two cavities. Such nonclassical states and their decoherence due to cavity dissipation could be studied by performing atom correlation experiments.

A new experimental limit to the possible time variation of the proton gyromagnetic ratio times the electron-to-proton mass ratio has been obtained from the frequency comparison data between Cs and Mg atomic beam standards. The measurements, made over a period of one year, lead to an upper limit for the rate of change of ${\mathit{g}}_{\mathit{p}}$(${\mathit{m}}_{\mathit{e}}$/${\mathit{m}}_{\mathit{p}}$) of 5.4×${10}^{\mathrm{-}3}$/yr. This result, based only on the validity of the quantum mechanical theory of the atomic spectra, together with astrophysical data regarding analogous products of atomic fundamental constants, leads also to a new limit for the time stability of the fine structure constant α (2.7×${10}^{\mathrm{-}13}$/yr).

Classical periodic orbits are stationary-phase points in path integral representations of quantum propagators. We show that complex solutions of the stationary-phase equation, not corresponding to real classical periodic orbits, give additional contributions to the propagator which can be important, especially near bifurcations. We reveal the existence and relevance of such periodic ghost orbits for a kicked top.

A semiclassical method is discussed for propagating wave packets that incorporates nonlinear classical dynamical information through the use of multiple reference trajectories. We apply the theory to obtain an analytic approximation for the autocorrelation function in the Coulomb potential which is extremely accurate in many circumstances in spite of the Coulomb singularity. All the detailed quantum behavior is reproduced including the long time revivals and the spectrum. The evolving phase space structure of the classical analog reveals how well a particular case will be approximated.

We investigate the magnetized Bose gas at temperatures above pair threshold. New magnetization laws are obtained for a wide range of field strengths, and the gas is shown to exhibit the Meissner effect. Some related results for the Fermi gas, a relativistic paramagnet, are also discussed.

We study the trajectories followed by a particle weakly perturbed by noise, when escaping from the domain of attraction of a stable fixed point. If the particle’s stationary distribution lacks detailed balance, a focus may occur along the most probable exit path, leading to a breakdown of symmetry (if present). The exit trajectory bifurcates, and the exit location distribution may become ‘‘skewed’’ (non-Gaussian). The weak-noise asymptotics of the mean escape time are also affected. Our methods extend to the study of skewed exit location distributions in stochastic models without symmetry.