It is shown that translational disorder in the interior bulk of real sandpiles is a relevant perturbation on self-organized surface fluctuations. In two simplified models, this disorder destroys the flat phase of the surface; surface fluctuations are instead described at long wavelengths for all parameter values by a simple diffusion equation with noise, which implies a logarithmically rough surface in d=2. This result suggests that real sandpiles may also be described by a simple diffusion equation, and proves that bulk translational disorder is important for their surface fluctuations.

We calculate the partition function for a relativistic Bose-Einstein gas. The excitation energies are identified and compared with known results in various limits. In particular, this treatment shows how the Goldstone bosons of a spontaneously broken symmetry and the quasiparticles of the nonrelativistic gas emerge as special cases of one general formula. New results are obtained for the spectrum of Goldstone modes in a medium of nonzero density, and the fully relativistic case is discussed along with a possible cosmological application.

The semiclassical two-anyon partition function is shown to give the exact answer for the quantum second virial coefficient of an anyonic gas. The same method, when extended to the semiclassical three-anyon partition function, yields a remarkably simple result. The implications and the limitations of the method are pointed out.

Quasienergy eigenstates are constructed for a quantum harmonic oscillator with a periodic, time-dependent ‘‘spring constant.’’ This is done by a sequence of canonical transformations. The wave function in the new variables is that of an ordinary oscillator.

We present a new cluster-update Monte Carlo algorithm for a fluctuating interface in the 3D Ising model. Critical slowing down is drastically reduced and the dynamical critical exponent at the roughening temperature of the 3D Ising model is found to be ${\mathit{z}}_{\mathrm{cl}}$=0.44±0.03. For the Metropolis algorithm we obtain ${\mathit{z}}_{\mathrm{Met}}$=2.0±0.1 while the Swendsen-Wang algorithm performs even worse than local updating. A new method which suppresses fluctuations in the two bulk phases is introduced to determine moments of the interfacial thickness.

The scaling dimensions and the asymptotic behavior of correlation functions of the main operators in a continuous model of a spinless 1D Bose or Fermi gas with a rather general pairwise interaction are obtained using finite-size effects.

I show that Weinberg’s nonlinear quantum mechanics leads either to communication via Einstein-Podolsky-Rosen correlations, or to communications between branches of the wave function.

We explore possible distinctions between multifractal scaling phenomena and Lagrangian field theories (FT’s) describing standard critical phenomena, via the operator-product expansion. While the scaling dimensions ${\mathit{x}}_{\mathit{n}}$ of multifractal moments must be convex functions of the order n, analogous FT exponents of powers of the field are concave, by stability and correlation inequalities, and cannot describe multifractal scaling. However, powers of gradients of the field may lead to a novel and unexpected multifractal convexity in a FT, such as, e.g., the nonlinear σ model.

We propose an experiment which demonstrates the nonlocal properties of a singe-photon field via phase-sensitive measurements. This is the first proposal which demonstrates nonlocality and a violation of Bell’s inequality with a single photon rather than a correlated photon pair.

We discuss the possibility that different realms of physics are described by distinct quantization constants. From the consistency of existing data, we infer limits on the differences between hypothetically distinct quantization constants for different elementary particles. Since the existence of multiple Planck constants implies violations of space-time symmetries, these limits may be viewed as precise tests of fundamental conservation laws, including the conservation of linear momentum and energy.

We develop high-temperature expansions for the conformal charge c of the square-lattice-Ising and three state-Potts models using Cardy’s expression for c in terms of the second moment of the energy-energy correlation function. Using Padé and integral approximant methods to analyze the series, we estimate its value to be 0.500±0.001 and 0.80±0.01 for the Ising and three-state-Potts models, respectively. In addition, we show that the conformal charge can be bounded in terms of another universal amplitude ratio

A family of Hilbert spaces with a positive-definite inner product is constructed which interpolates analytically between the Fock spaces representing Fermi and Bose particles. It is shown that the physically unallowed subspaces in the two limiting cases correspond to the appearance of states of zero norm.

The effect of external white Gaussian noise on the invariant measure of a periodically driven damped nonlinear oscillator is studied by solving for the first time the full three-dimensional Fokker-Planck equation by numerical means. We critically discuss and interpret deterministic concepts and stochastic notions in the presence of noise and chaos.

We study the bound-state spectrum of many particles obeying fractional statistics (anyons) in a two-dimensional system in the presence of an external potential and a large magnetic field B. As a function of B, there occur periodic recurrences of quantized states at fixed energy. For fixed particle number, the period is determined by the fractional charge, while at fixed chemical potential, the fractional charge is masked by the fractional statistics. We discuss the relevance of these results to recent experiments in quantum Hall devices, and we propose a simple extension of these experiments which could measure the fractional statistics.

Two examples are given that substantially simplify the no-hidden-variables theorem of Kochen and Specker, greatly reducing the number of observables considered and requiring no intricate geometric argument. While one of the examples also obeys a more powerful version of Bell’s theorem, the other does not. The examples provide a new perspective on both of these fundamental theorems and on the relation between them.

We have achieved control of chaos in a physical system using the method of Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)]. The method requires only small time-dependent perturbations of a single-system parameter and does not require that one have model equations for the dynamics. We demonstrate the power of the method by controlling a chaotic system around unstable periodic orbits of order 1 and 2, switching between them at will.

A method is developed which uses the exponential sensitivity of a chaotic system to tiny perturbations to direct the system to a desired accessible state in a short time. This is done by applying a small, judiciously chosen, perturbation to an available system parameter. An expression for the time required to reach an accessible state by applying such a perturbation is derived and confirmed by numerical experiment. The method introduced is shown to be effective even in the presence of small-amplitude noise or small modeling errors.

The oscillations of a linear triatomic molecule with the first atom driven at a constant velocity v are studied numerically. As v increases, we observe a sequence of transitions from quasiperiodicity to chaos, mode locking, chaos, another mode locking, then to chaos before the atoms break off. The largest Lyapunov exponent does not rise linearly with the driven velocity. The mode-locking structure for the last onset to chaos has a universal fractal dimension 0.871±0.001 at a winding number far from the golden mean.

A model for dense packings of disks rolling on each other is presented. This model might have application for turbulence, tectonic motion, and mechanical gearworks. A full classification of solutions with fourfold loops is given. The fractal dimensions are calculated and compare favorably with Kolmogoroff scaling of turbulence.

The (2+1)-dimensional Davey-Stewartson I system is quantized, and the exact eigenvalues and eigenfunctions of the Hamiltonian are obtained. Thermodynamic quantities are also given. Although it is quantized by using the commutation relations for bosons, the energy spectrum and thus the thermodynamic quantities reveal the characteristics of a system with two species of independent fermions.