We formulate one-dimensional many-body integrable systems in terms of a new set of phase space variables involving exchange operators. The Hamiltonian in these variables assumes a decoupled form. This greatly simplifies the derivation of the conserved charges and the proof of their commutativity at the quantum level.

An analytic expression is derived for the Lyapunov exponents of the product of random transfer matrices related to the Ising model with quenched disorder in one dimension. We find a deterministic map which transforms the original system to a new one with zero external field and constant coupling. The free energy and the rate of correlation decay are thus obtained in terms of an exponentially convergent series. Our results can be generalized to the product of random matrices with nonzero entries.

In this Letter we report a new construction to obtain restricted solid-on-solid (RSOS) models out of loop models. The method is a generalization of ideas developed by Owczarek and Baxter, and by Pasquier. In particular we consider a solvable O(n) model and point out that some of the RSOS models thus obtained admit an off-critical extension. Among these models we find a spin-1 Ising model, which is solvable not only at the critical point, but also in a fieldlike deviation away from it. We calculate the critical exponent δ=15 directly from the relation between the free energy and the field. This is the first determination of this exponent without the use of scaling relations.

We investigate the influence of the measure in the path integral for Euclidean quantum gravity in four dimensions within the Regge calculus. The action is bounded without additional terms by fixing the average lattice spacing. We set the length scale by a parameter β and consider a scale-invariant and a uniform measure. In the low-β region we observe a phase with negative curvature and a homogeneous distribution of the link lengths independent of the measure. The large-β region is characterized by inhomogeneous link length distributions with spikes and positive curvature depending on the measure.

We explore the impact of astrophysical uncertainties on the Mikheyev-Smirnov-Wolfenstein (MSW) solution by calculating the allowed MSW solutions for 1000 different solar models with a Monte Carlo selection of solar model input parameters, assuming a full three-family MSW mixing. Applications are made to the chlorine, gallium, Kamiokande, and Borexino experiments. The initial GALLEX result limits the mixing parameters to the upper diagonal and the vertical regions of the MSW triangle. We also calculate the expected event rates in the Borexino experiment assuming the MSW solutions implied by GALLEX.

We write down a local ${\mathrm{CP}}_1$ model involving two gauge fields, which is exactly equivalent to the O(3) σ model with the Hopf term. We impose the ${\mathrm{CP}}_1$ constraint by using the Gaussian representation of the delta function. For the coefficient of the Hopf term, θ= π / 2s ,2s being an integer, we show that the resulting model is exactly equivalent to an interacting theory of spin-s fields. Thus we conjecture that there should be a fixed point in the spin-s theory near which it is exactly equal to the σ model.

A detailed analysis of predictions of SU(5) supergravity grand unification within the framework of radiative breaking of SU(2)×U(1) is given. The masses of the 31 new supersymmetric particles depend on only four parameters. The full parameter space is explored and found to be strongly restricted by proton decay bounds if one requires no extreme fine tuning and the Higgs triplet mass to be ≤3${\mathit{M}}_{\mathit{G}}$. The 31 sparticle masses are then strongly correlated, e.g., ${\mathit{m}}_{\mathit{W}\mathrm{̃}1}$≲1/3${\mathit{m}}_{\mathit{g}\mathrm{̃}}$, ${\mathit{m}}_{\mathit{W}\mathrm{̃}1}$≃${\mathit{M}}_{\mathit{Z}\mathrm{̃}2}$≃2${\mathit{m}}_{\mathit{Z}\mathrm{̃}1}$, ${\mathit{m}}_{\mathit{h}}$≲110 GeV.

Lattice gauge theory techniques have recently achieved sufficient accuracy to permit a determination of the strong coupling constant from the 1P-1S splitting in the charmonium system, with all systematic errors estimated quantitatively. The present result is ${\mathrm{\alpha }}_{\mathrm{MS}\mathrm{¯}}$(5 GeV)=0.174±0.012, or equivalently, ${\mathrm{\Lambda }}_{\mathrm{MS}\mathrm{¯}}^{\mathrm{}\left(4\right)\mathrm{}}$=${160}_{\mathrm{-}37}^{+47\mathrm{}}$ MeV (MS¯ denotes the modified minimal subtraction scheme).

A search for the decay ${\mathrm{\pi }}^0$→γX, where X is any long-lived weakly interacting neutral vector particle with mass smaller than the neutral pion pass, was performed using neutral pions tagged by ${\mathit{K}}^{+}$→${\mathrm{\pi }}^{+}$${\mathrm{\pi }}^0$. A 90%-C.L. upper limit for the branching ratio of the two-body decay B(${\mathrm{\pi }}^0$→γX)<5×${10}^{\mathrm{-}4}$ is set. Limits are also set for three-body decays ${\mathrm{\pi }}^0$→γXX’.

We apply a recently computed nucleation rate to a first-order deconfinement/chiral-symmetry restoring phase transition in a set of rate equations to study the time evolution of expanding quark-gluon plasma as it converts to hadronic matter. At energies of the BNL Relativistic Heavy Ion Colliders, the system must supercool about 20% below ${\mathit{T}}_{\mathit{c}}$ before nucleation of hadronic bubbles is sufficiently rapid to overcome the expansion rate. The system reheats to near ${\mathit{T}}_{\mathit{c}}$, nucleation turns off, and the transition is completed by the growth of previously nucleated bubbles. Based on Bjorken hydrodynamics and on current parameter values, we estimate that the transition generates 30% extra entropy.

It is shown that self-similar behavior in multiplicity fluctuations exists in the Ginzburg-Landau description of second-order phase transitions. Furthermore, there exists a numerical exponent that characterizes the intermittency properties in the hadronic phase and is independent of the specific values of the coefficients in the Ginzburg-Landau potential. Current data on intermittency are only 2σ away from the critical exponent.

The mass, energy, and centrality dependence of rapidity density distributions of relativistic, charged particles, produced in heavy-ion interactions in the energy range 4A–200A GeV, are investigated. The results indicate that the rapidity density distributions show systematic variations, which are used to predict distributions for Au+Au and Pb+Pb interactions in a model-independent way.

The ground-state energy of an atom of nuclear charge Ze and in a magnetic field B is evaluated exactly in the asymptotic regime Z→∞. We show rigorously that there are five regions as Z→∞: B≪${\mathit{Z}}^{4/3}$, B≊${\mathit{Z}}^{4/3}$, ${\mathit{Z}}^{4/3}$≪B≪${\mathit{Z}}^3$, B≊${\mathit{Z}}^3$, B≫${\mathit{Z}}^3$. Different regions have different physics and different asymptotic therories. Regions 1,2,3,5 are described exactly by a simple density-functional theory, but only in regions 1,2,3 is it of the semiclassical Thomas-Fermi form. Region 4 cannot be described exactly by any simple density-functonal theory; surprisingly, it can be described by a simple density matrix functonal theory.

We descrbe a new method for measuring excited-state collisions between optically trapped atoms. With this method, trap-loss collision rates are deduced from the loading behavior of clouds of trapped atoms in the regime where radiation trapping limits the atom density. Our measurements indicate that ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ trap-loss collisions occur at significantly smaller rates than expected both from previous work on Cs and from recent models. In addition, the dependence of the trap-loss collisions on the frequency of the light used to excite the atom pairs is also different from that of Cs, suggesting that assumptions about the dynamics in these models need modification.

The relaxation rates of the monopole, magnetic dipole, and electric quadrupole moments have been determined for the $3^1$P state of helium excited by electron impact, The data are determined from atomic lifetimes using linear and circular polarization analyzed radiation with the electron-photon delayed coincidence technique. This has permitted the direct observation of the time dependence of all the off-diagonal elements of the density matrix of the excited state. The implications for atomic state information determined from polarization and angular correlation methods are indicated.

We discuss the explicit dependence of the final trajectory on initial conditions for randomly driven nonlinear dynamical systems which are stopped and restarted with random velocities at regular intervals (a Brownian-type motion). We find a transtion from chaotic behavior for long intervals between stops to nonchaotic behavior for short intervals between stops. For short intervals, the Lyapunov exponent is related to the thermal average square force due to the potential. The consequences for ‘‘hybrid molecular-dynamics Monte Carlo’’ sampling methods are discussed.

We present an experimental study of resonance frequencies of a diphasic medium that consists of diethyl ether containing vapor bubbles. We show that the liquid-vapor transfers affect the sound velocity and attenuation so that the usual liquid-gas effective-medium theory is in error at low frequency. The measurements of resonance frequency and attenuation can be used to estimate the vapor volume fraction and the bubble diameter. At high sound amplitude the shape of the resonance curves shows nonlinear effects, and acoustic bistability is observed.

The Kolmogorov relation for the third-order moments of the velocity differences is generalized for the case of statistically steady turbulence and applied to the Bénard convection problem. The predicted temperature and velocity spectra are ${\mathit{E}}_{\mathit{T}}$≊${\mathit{k}}^{\mathrm{-}7/5}$ and E≊${\mathit{k}}^{\mathrm{-}11/5}$, respectively. At the smaller scales, in the dissipation range of the temperature fluctuations, the Kolmogorov range where most of the energy is dissipated is predicted. The new set of scaling exponents, which can be observed in the experiments in the small-aspect-ratio convection cells, is derived.

When an intense, plane-polarized, laser pulse interacts with a plasma, the relativistic nonlinearities induce a third-harmonic polarization. A phase-locked growth of a third-harmonic wave can take place, but the difference between the nonlinear dispersion of the pump and driven waves leads to a rapid unlocking, resulting in a saturation. What become third-harmonic amplitude oscillations are identified here, and the nonlinear phase velocity and the renormalized electron mass due to plasmon screening are calculated. A simple phase-matching scheme, based on a resonant density modulation, is then proposed and analyzed.

The concentration profiles of carboxy-terminated polystyrene chains in the melt grafted onto oxide-covered silicon substrates were measured using secondary-ion mass spectroscopy. The grafting density increased with temperature and an enthalpy of +7.4 kcal/mole was deduced for the grafting reaction, SiOH+R(COOH)⇄R(COOSi)+${\mathrm{H}}_2$O. Relatively high grafting densities (σ∼6.6 mg/${\mathrm{m}}^2$) were achieved with minimal chain distortion or displacement of long chains by shorter ones. Significant stretching of the grafted chains occurred for σ>10 mg/${\mathrm{m}}^2$. An equilibrium constant for the grafting reaction incorporating entropy is discussed.