The natural integrable correlated strongly coupled boson system in 1 + 1 dimensions is the $q$-boson hopping model; we calculate its critical exponent $\theta$ and determine its correlation functions. For small couplings the $q$-boson model has natural connections with the Bose gas and the $\mathrm{XY}$ models of very large spin for which $\theta \text{'}\mathrm{s}$ and correlators are reported. For large couplings the hopping model is a new phase of interacting bosons substantially different from the impenetrable Bose gas.

A new link invariant is obtained using the exactly solvable chiral Potts model and a generalized Gaussian summation identity. The new link invariant is characterized by roots of unity and does not appear to belong to the usual quantum group family of invariants. The invariant is given in terms of a matrix associated with the link diagram, and can be readily written down for any given link.

The ${}_{}{}^7{}_{}{}^{}\mathrm{Li}{(\overrightarrow{p},\gamma )}^8\mathrm{Be}$ reaction has been studied using polarized protons having an incident energy in the range $E_p\left(\mathrm{lab}\right)=80-0\mathrm{}$ keV. The measured angular distributions of the cross section $\frac{\sigma \left(\theta \right)}{A_0}$ and analyzing power $A_y\left(\theta \right)$ were interpreted using a model independent transition-matrix element analysis. The large (Å40%) analyzing power at 90° indicates the presence of an appreciable $p$-wave capture strength at these energies. The direct-capture model is used to show that this could reduce the astrophysical $S$ factor by as much as 40%.

The problems of the partial covering time (PCT) and of the random covering time (RCT) are studied in two dimensions using Monte Carlo simulations. We find that the PCT (RCT) presents a discontinuous transition at f=1 (f=0), where f is the fraction of visted sites by a random walker. An analysis of the time evolution of the surviving unvisited clusters reveals that they exhibit a time-dependent fractal-like structure.

We show that Haldane’s new definition of statistics, when generalized to infinite dimensional Hilbert spaces, is determined by the high temperature limit of the second virial coefficient. We thus show that this exclusion statistics parameter g of anyone is nontrivial and is completely determined by its exchange statistics parameter α. We also compute g for quasiparticles in the Luttinger model and show that it is equal to α.

The problem of separating n linearly superimposed uncorrelated signals and determining their mixing coefficients is reduced to an eigenvalue problem which involves the simultaneous diagonalization of two symmetric matrices whose elements are measureable time delayed correlation functions. The diagonalization matrix can be determined from a cost function whose number of minima is equal to the number of degenerate solutions. Our approach offers the possibility to separate also nonlinear mixtures of signals.

By finding measurements that optimally resolve neighboring quantum states, we use statistical distinguishability to define a natural Riemannian metric on the space of quantum-mechanical density operators and to formulate uncertainty principles that are more general and more stringent than standard uncertainty principles.

We present a new methodology for deriving physically important exact solutions of certain nonintegrable equations. These solutions describe the nonlinear interaction of traveling waves. Examples include multishock and multisoliton solutions.

The (220) lattice spacing of a silicon crystal was measured by combined x-ray and optical interferometry to about 3×${10}^{\mathrm{-}8}$ relative accuracy. The value obtained is ${\mathit{d}}_{220}$=192015.551±0.005) fm. After correcting for the impurity-induced lattice contraction, ${\mathit{d}}_{220}$=192015.569±0.006 fm is obtained

We study the dynamics of a system of bosonic or fermionic atoms in a microscopic trap undergoing laser cooling. We show that the stationary state can be described by a Bose-Einstein or Fermi-Dirac distribution, respectively. Fluorescence from the system reflects quantum statistical properties.

We prove that in an exact, unrestricted Hartree-Fock calculation each energy level of the Hartree-Fock equation is either completely filled or completely empty. The only assumption needed is that the two-body interaction is—like the Coulomb interaction—repulsive; it could, however, be more complicated than a simple potential; e.g., it could have tensor forces and velocity dependence. In particular, the Hartree-Fock energy levels of atoms and molecules, often called shells, are never partially filled.

Ratchetlike devices can rectify symmetric, unbiased nonequilibrium noise resulting in fluctuation-induced currents. We study some simple models to investigate the dependence of a nonequilibrium steady-state current on the characteristic features of the ratchet and the applied noise. It turns out that the magnitude and the direction of the induced current depend not only on the shape of the ratchet, but also on the statistics of the fluctuations.

We study stochastic resonance in a bistable system which is excited simultaneously by white and harmonic noise which we understand as the signal. In our case the spectral line of the signal has a finite width as it occurs in many real situations. Using techniques of cumulant analysis as well as computer simulations we find that the effect of stochastic resonance is preserved in the case of harmonic noise excitation. Moreover we show that the width of the spectral line of the signal at the output can be decreased via stochastic resonance. The last could be of importance in the practical using of the stochastic resonance.

Resonators driven to self-oscillation via active feedback play an important role in technology. Among the stochastic processes driving phase diffusion in such oscillators is noise from the feedback amplifier. Here a technique is described by which phase diffusion due to this noise can be suppressed. We have achieved a 10 dB reduction in phase diffusion by using the technique on an oscillator whose frequency-controlling element is a nonlinear mechanical resonator. The technique, in principle, provides a quantum nondemolition method of tracking a resonator’s phase.

Uncoupled, classical Maxwell-Chern-Simons theory is studied in regions in which the Chern-Simons coefficient is a spacetime dependent quantity. Gauge invariance demands a modification of the strict Chern-Simons form in such a region. Behavior is governed by boundary and initial conditions. In many cases, the resulting classical behavior qualitatively resembles diffusive processes in statistical systems.

We study the fluctuations of the probability density P(r,t) of diffusing particles to be at distance r at time t in the presence of random potentials, represented by random transition rates. We find an exact relation which expresses all the moments of P(r,t) in terms of its first moment, for both quenched and annealed disorder and for any dimension. From this relation follows that anomalous diffusion implies nontrivial behavior of the moments of P(r,t), such as an exponential divergence of the relative fluctuations for large r.

We present a new method for optimization: constrained global optimization (CGO). CGO iteratively uses a Glauber spin flip probability and the Metropolis algorithm. The spin flip probability allows changing only the values of variables contributing excessively to the function to be minimized. We illustrate CGO with two problems—Thomson’s problem of finding the minimum-energy configuration of unit charges on a spherical surface, and a problem of assigning offices—for which CGO finds better minima than other methods. We think CGO will apply to a wide class of optimization problems.

Santos argues that, if one interprets probabilities as ratios of detected events to copies of the physical system initially prepared, the quantum mechanical predictions for the classic tests of Bell’s inequalities do not violate the inequalities. Furthermore, he suggests that quantum mechanical states which do violate the inequalities are not physically realizable. We discuss a physically realizable experiment, meeting his requirements, where quantum mechanics does violate the inequalities.

The question whether systems having the same set of metastable states have identical Hamiltonian and hence identical dynamics is addressed and examined for various classical spin systems. The answer depends on the number of metastable states and on the distribution of the local fields for small fields. The rule that static properties determine dynamical properties is found to be applicable for a large class of random systems, almost any random system in the mean-field limit and many random systems in finite number of dimensions.

The autocorrelation function of a periodically driven bistable system is considered in the limit of weak noise. We predict a broad window in the Fourier spectrum with a universal (power law) decay of the spectral density, accompanied by dips of finite width at the second and fourth harmonics of the driving frequency. For higher driving frequencies the dips are replaced by peaks of finite though extremely narrow width. Analytical results are confirmed by numerical studies and are used to analyze previous experimental data.