We present a method which allows calculation of whole universal finite-size-scaling functions from Monte Carlo data. The crux of the new method is a technique of isolating the singular part from the total free energy. We apply this method to the 3-state Potts model on a square lattice and find the normalized scaling function Y(x) in the form 1+x+5.31${\mathit{x}}^2$-1.2${\mathit{x}}^3$-0.67${\mathit{x}}^4$ . . . near the bulk critical point x=0, together with the normalizing universal amplitude E=1.053 and a nonuniversal metric factor D=-0.387. It also behaves as Y(x)≊(±x${)}^{\mathit{d}\nu }$${\mathit{Q}}_{\pm }$ for large x in agreement with the hyperuniversality hypothesis with ${\mathit{Q}}_{+}$/${\mathit{Q}}_{\mathrm{-}}$≊1.

It is shown that by including both the spin-up and spin-down components of a spin-1/2 field, a parity conserving Chern-Simons theory can be constructed. For a single fermion field the model contains (aside from the mass and a coupling constant) a parameter ε which can have the values ±1. It is shown that only the positive value allows an interpretation in terms of anyons. This result thus serves to sharpen the frequently overlooked distinction between the Chern-Simons interaction and the anyon. While the former can be introduced into any (2+1)-dimensional field theory, the latter is seen to be a special limiting case obtained only in those instances for which relativistic and spin considerations can be ignored.

We consider a kicked system on the cylinder obtained upon quantization of a chaotic area-preserving map. We use the thermodynamic formalism to investigate the scaling properties of the fractal spectrum. In time evolution we observe anomalous diffusion with an exponent closely related to the Hausdorff dimension of the spectrum, and dependent upon the parameters of the system.

Dynamics involving a discrete second-order time derivative captures many essential, previously unexplained features of the collective behavior of complex, spatially extended systems such as cellular automata and coupled-map lattices. We argue that irrational frequencies can emerge from discrete-time dynamics, and that the second-order dynamics makes previous droplet-type arguments irrelevant for these models. These findings are supported by numerical examples.

The concept of adiabatic invariance in one-dimensional Hamiltonian systems H(p,q;λ) is generalized to include the case when the time derivative of the slowly varying parameter λ is given by λ̇=f(H,λ)φ(q,p), where f and φ are arbitrary functions, and q and p are the canonical coordinates.

The Einstein-Podolsky-Rosen paradox is demonstrated experimentally for dynamical variables having a continuous spectrum. As opposed to previous work with discrete spin or polarization variables, the continuous optical amplitudes of a signal beam are inferred in turn from those of a spatially separated but strongly correlated idler beam generated by nondegenerate parametric amplification. The uncertainty product for the variances of these inferences is observed to be 0.70±0.01, which is below the limit of unity required for the demonstration of the paradox.

According to the de Broglie pilot wave theory, a pilot wave which is empty of photons is still capable of physical effects like induced coherence. We have carried out an experiment to test this prediction. The experiment involves interference of photons produced by down-conversion in two nonlinear crystals and depends on the mutual coherence induced between the two signal beams by an idler. When the photon is removed from the idler by a beam splitter, it is found that the resulting ‘‘empty pilot wave’’ no longer induces coherence. This violates at least the Selleri-Croca version of the de Broglie pilot wave theory makes the physical reality of the corresponding pilot wave doubtful.

The stochastic Landau equation for a periodically driven process with either two discretely degenerate attractors or a continuum of degenerate attractors is studied for small noise. We calculate analytically the probability ${\mathit{P}}^{\mathrm{tr}}$ for the transition between the attractors leading to phase diffusion in the continuous case. Our results are in good agreement with numerical simulations and in the discrete case also with experiments on periodically driven Rayleigh-Bénard convection. They explain the sensitive dependence of ${\mathit{P}}^{\mathrm{tr}}$ on the equation’s parameters.

Although originally thought to show great promise in solving quantum many-body problems on a lattice, numerical real-space renormalization-group techniques have had little success for such problems. We explore the nature of the difficulties involved by studying the applicaton of the method to the simple tight-binding model in one dimension. The standard approach fails dramatically for this model. We show that the key to successfully applying the renormalization-group technique lies in applying a variety of boundary conditions to a block in order to simulate the effect of neighboring blocks.

We examine quantum chaotic scattering in the semiclassical regime for the two cases where the classical scattering is hyperbolic and nonhyperbolic. It is shown that in the nonhyperbolic case the energy-dependent S-matrix autocorrelation function C(ɛ) exhibits a cusp-shaped peak at ɛ=0 (where ɛ denotes the energy difference). This indicates that the fine scale fluctuations with energy of the S matrix are characteristically greatly enhanced in the nonhyperbolic case as compared with the hyperbolic case.

Coupled map lattices with asymmetric short-range couplings are studied analytically and numerically. It is shown that with open boundary conditions these systems exhibit spatially uniform, but temporally chaotic states that are stable even in the thermodynamic limit. The stability of this state is associated with the appearance of a gap at zero wave number in the spectrum of the linear operator describing the fluctuations about the uniform state. The long-range order is unstable to noise. We calculate the finite coherence length of the chaotic state in the presence of weak noise.

We study an origin of avoided crossings for classically nonintegrable systems. Using a diabatic transformation, we show that characteristic features of ‘‘scars’’ continuously change along diabatic lines. Moreover, through Fourier transformation of an energy level density, we suggest that avoided crossings in fully chaotic systems originate from the long periodic orbits winding around scars.

The escape and synchronization of a 1-μm Brownian particle from an optical trap is presented. The probability distribution of residence times within a given well is exponential with a cutoff at short time. Temporal modulation of the well leads to synchronization.

We examine the spatiotemporal dynamics of the nonlinear three-wave interaction describing the saturation of an unstable wave by coupling to two damped waves. We observe spatiotemporal chaos involving coherent structures that are characterized by temporal and spatial scales determined by the parameters in the problem.

We describe a new method to set an upper limit of the photon mass ${\mathit{m}}_{\gamma }$ at low temperatures, based on a null test of Ampère’s law. The result of our measurements, expressed as the upper limit of the photon mass at 1.24 K, is ${\mathit{m}}_{\gamma }$≤(8.4±0.8)×${10}^{\mathrm{-}46}$ g.

We show that mixed states can produce maximal violations in the Bell inequality due to Clauser, Horne, Shimony, and Holt (CHSH). This follows from the degeneracy of the operator which is naturally associated with the Bell inequality (here called the Bell operator). We have calculated the form of all the eigenvalues for the generic CHSH Bell operator. Finally, we consider several examples which demonstrate the utility of studying the eigenvalues and eigenvectors of the Bell operator.

The solution of the initial-boundary-value problem of integrabale nonlinear evolution equations, with the spatial variable on a half-infinite line, can be reduced to the solution of a linear intregral equation. The asymptotic analysis of this equation for large t shows how the boundary conditions can generate solitons.

Quantum techniques for key distribution—the classically impossible task of distributing secret information over an insecure channel whose transmissions are subject to inspection by an eavesdropper, between parties who share no secret initially—have been proposed using (a) four nonorthogonally polarized single-photon states or low-intensity light pulses, and (b) polarization-entangled or spacetime-entangled two-photon states. Here we show that in principle any two nonorthogonal quantum states suffice, and describe a practical interferometric realization using low-intensity coherent light pulses.

We show that a large class of Fokker-Planck equations, like the Schrödinger equation, can exhibit a transition in their spectral statistics as a coupling parameter is varied. We assert that this transition is connected to the transition to nonintegrability in a particular set of Hamilton’s equations. In the case of the Schrödinger equation, this transition is known to be a fingerprint of the underlying classical dynamics. However, the Hamilton’s equations describing the transition in the Fokker-Planck spectrum have no direct physical relation to the underlying dynamics of the Fokker-Planck equation, and consequently have no such simple physical interpretation.

We use supersymmetric quantum mechanics to show that the spectrum of three anyons in a harmonic potential exhibits an almost complete mirror symmetry about semions. Barring a subset of exactly solved states, all states come in pairs such that the energy of one state with the statistics parameter θ is equal to the energy of its partner state at π-θ. Bosons, semions, and fermions have θ=0,π/2, and π, respectively. From this, we show that the third virial coefficient of an ideal anyon gas is exactly mirror symmetric about semions.