We present exact solutions for breather solitons in the (2+1)-dimensional Chern-Simons gauge theory with external magnetic field B. The breather soliton is a time-dependent solution whose size is oscillating and whose center of mass moves ina cyclotron motion. These solitions describe how the Jackiw-Pi solitons behave in the external magnetic field. We then apply the Bohr-Sommerfeld semiclassical quantization to the breathing mode and the cyclotron motion. It is found that the orbital angular momentum takes on an integer value and that the quantum soliton is in the Landau level.

Vortex solitons of the planar, gauged nonlinear Schrödinger equation are quantized semiclassically in the presence of an external magnetic field.

We relate the complex solutions of the thermodynamic Bethe-ansatz equations to the excited states in factorizable massive models. This approach permits one to recover exactly the ultraviolet behavior of these excitations. In order to illustrate our method we consider several unitary and nonunitary integrable models. We also comment on the calculation of critical exponents in massless integrable models.

The set of orientations of a measuring device (e.g., a Stern-Gerlach magnet) produced by the action of a Lie group constitutes a honmogeneous space S (e.g., a sphere). A hidden-variable measure determines a metric D on S, the triangle inequality being Bell’s inequality. But identification of S with Hilbert-space projectors induces a locally convex metric d on S. The Einstein-Podolsky-Rosen (EPR) hypotheses imply that D=${\mathit{d}}^2$, which is impossible because the square of a locally convex metric cannot be a metric. This proves the Bell-EPR theorem. Classical systems avoid the contradiction by allowing only values d=0,1. The ‘‘watchdog’’ effect is shown to result from the form of the quantum-mechanical metric.

It has been shown that two correlated photons incident upon two distant interferometers can give a coincidence counting rate that depends nonlocally on the sum of the phases of the two interferometers. It is shown here that the results of existing experiments violate a simple inequality that must be satisfied by any classical or semiclassical field theory. The inequality provides a graphic illustration of the lack of objective realism of the electric field.

We consider the statistical mechanics of an interacting anyon gas with a repulsive pair potential of the form g/${\mathit{r}}^2$. The second virial coefficient is calculated and shown to be a smooth function of the statistical parameter α for g>0, without the cusps previously found at the Bose point in a noninteracting anyon gas. As g→0 the cusps remain absent but a different type of singularity develops at the Bose point, showing that the order of limits is crucial.

One-dimensional critical quantum sytems have a universal, intensive ‘‘ground-state degeneracy,’’ g, which depends on the universality class of the boundary conditions, and is in general noninteger. This is calculated, using the conjectured boundary conditions corresponding to a multichannel Kondo impurity and shown to agree with Bethe-ansatz results. g is argued to decrease under renormalization from a less stable to a more stable critical point and plays a role in boundary critical phenomena quite analogous to that played by c, the conformal anomaly, in the bulk case.

We study properties of interfaces between stationary phases of the two-dimensional discrete-time Toom model (north-east-center majority vote with small noise): phases not described by equilibrium Gibbs ensembles. Fluctuations in the interface maintained by mixed boundary conditions grow with distance much slower than in equilibrium systems; they have exponents close to 1/4 or 1/3, depending on symmetry, rather than 1/2, and have long-range correlations reminescent of self-organized critical behavior. Approximate theories reproduce this behavior qualitatively and lead to novel nonlinear partial differential equations for the asymptotic profile.

We study the change of quantum spectra under two types of perturbations. One of them corresponds to the breaking of classical integrability and amounts to a crossover from level clustering to level repulsion. The second type of perturbation breaks time-reversal invariance; under conditions of classical chaos the degree of level repulsion then grows from linear to quadratic. To characterize the spectral changes we propose, for each type of transition, a distribution of nearest-neighbor spacings. Both of these ‘‘generalized Wigner surmises’’ are rigorous for suitable ensembles of 2×2 matrices but prove reliable for dynamical systems with many levels.

We propose a new method to compute Lyapunov exponents from limited experimental data. The method is tested on a variety of known model systems, and it is found that the algorithm can be used to obtain a reasonable Lyapunov-exponent spectrum from only 5000 data points with a precision of ${10}^{\mathrm{-}1}$ or ${10}^{\mathrm{-}2}$ in three- or four-dimensional phase space, or 10 000 data points in five-dimensional phase space. We also apply our algorithm to the daily-averaged data of surface temperature observed at two locations in the United States to quantitatively evaluate atmospheric predictability.

The concept of a nonequilibrium potential is applied to dynamical systems with fractal attractors or repellers. In particular, we study the case of the Feigenbaum attractor in one-dimensional maps and the case of hyperbolic strange attractors or repellers in two-dimensional maps. The potential-height distribution of the latter is shown to exhibit multifractal features; that of the Feigenbaum attractor is characterized by a single number, the universal exponent for noisy period-doubling bifurcations.

We show that multifractal measures arising from the symbolic dynamics of chaotic systems can be reproduced using iterated-functions system involving Möbius maps. This powerful approximation scheme is exact for hyperbolic billiards: The coding measures of zero-angle N-sided polygonal billiards are exactly rendered by N-1 Möbius maps. We also approximate with success the coding measures for the anisotropic Kepler system.

Geometric phases play an important role in the asymptotic behavior of multicomponent wave fields, such as electromagnetic waves in plasmas or quantum-mechanical spinors, particularly in the problem of Bohr-Sommerfeld quantization. The proper gauge independence of the eigenvalues and asymptotic wave functions can be understood in terms of gauge-invariant but noncanonical coordinates on the classical phase space.

Noise rise in the high-gain limit of a parametric magnetorestrictive amplifier is observed to occur close to the bifurcation point of the unperturbed strain dynamics. This work presents the first quantitative agreement between experimental results and the predicted universal scaling laws which relate the signal and noise gain to the bifurcation parameter. We also observe a scaling law, not predicted by the theory, in which the point of maximum signal gain shifts away from the bifurcation point as a function of the detuning with a critical exponent equal to -0.33 ±0.04.

An atomic interferometer based on a Young’s-type double-slit arrangement has been demonstrated. A supersonic beam of metastable helium atoms passes through a 2-μm-wide slit in a thin gold foil. This transversely coherent beam impinges on a second microfabricated transmission structure, consisting of two 1-μm-wide slits at a lateral distance of 8 μm. This double slit defines two possible paths on which the atoms can reach the detector slit. The good visibility of the observed fringes should make it possible to measure differential phase shifts in the interferometer of 1/3 rad in less than 10 min.

We have demonstrated an interferometer for atoms. A three-grating geometry is used, in which the interfering beams are distinctly separated in both position and momentum. We used a highly collimated beam of sodium atoms with a de Broglie wavelength of 16 pm and high-quality 0.4-μm-period free-standing gratings which we fabricated using a novel method. The interference signal is 70 counts/s, which allows us to determine the phase to 0.1 rad in 1 min. Applications of atom interferometers are briefly discussed.

The possibility of eliminating chaos in a dynamical system or of decreasing the leading Liapunov exponent by applying a weak periodic external forcing to the system is demonstrated through the example of a periodically driven pendulum. The applications of the external forcing also results in other striking changes in the dynamics such as a stabilization of narrow subharmonic steps and the achievement of very low winding numbers.

We present new results on the scaling of the ground-state energy ${\mathit{E}}_0$∝-${\mathit{N}}^{\mathrm{\beta }}$ for a neutral system with a large number (N) of locally interacting ‘‘charged’’ bosons in one dimension (1D). Variational methods provide an upper bound on β (β≤3) and lower bounds depending on the ratio of attraction to repulsion: β≥3, 5/3, and 1 when the ratio is >1, 1, and <1. It is argued that the lower bounds to β give the actual scaling laws. Connections to the 3D charged-boson gas and to 2D directed random paths in disordered media are discussed.

We investigate experimentally the scaling of the average time τ between intermittent, noise-induced bursts for a chaotic mechanical system near a crisis. The system studied is a periodically driven (frequency f) magnetoelastic ribbon. Theory predicts that for deterministic crises where τ scales as τ∼‖f-${\mathit{f}}_{\mathit{c}}$${\mathrm{\Vert }}^{\mathrm{-}\gamma }$ (f<${\mathit{f}}_{\mathit{c}}$, f=${\mathit{f}}_{\mathit{c}}$ at crisis), the characteristic time between noise-induced bursts (f≥${\mathit{f}}_{\mathit{c}}$) should scale as τ∼${\mathrm{\sigma }}^{\mathrm{-}\gamma }$g(‖f-${\mathit{f}}_{\mathit{c}}$‖/σ), where σ is the noise strength and γ is the same in both cases. We determine γ for the low-noise (‘‘deterministic’’) system, then add noise and observe that the scaling for τ is as predicted.

A general method to compute precise approximations to invariant tori of Hamiltonian systems is presented. For illustration, a strongly nonlinear example from accelerator theory is treated, in 21/2 degrees of freedom. Accuracy, computation time, and effectiveness near resonances are found to be highly favorable in comparison to previous methods.