We have measured the magnetic susceptibility, χ’+iχ’’, of the dilute dipolar-coupled Ising magnet ${\mathrm{LiHo}}_{0.045}$${\mathrm{Y}}_{0.955}$${\mathrm{F}}_4$ over six decades of frequency from 0.02 Hz to 20 kHz. The system behaves as an ideal relaxational glass with Arrhenius behavior in temperature of the peak in χ’’. Scaling data from T=100 mK to T=300 mK by the peak in χ’’ shows an enhanced low-frequency response at high temperatures, in contrast to expectations for spin-glasses and random-field magnets.

We consider the Landauer formula, relating conductances to transmission matrices, for a two-dimensional system in a magnetic field. We argue that the magnetoresistance, R, and the Hall resistance, ${\mathrm{R}}_{\mathrm{H}}$, satisfy the sum rule (R+${\mathit{R}}_{\mathrm{H}}$${)}^{\mathrm{-}1}$=(${\mathit{e}}^2$/h)Tr(${\mathit{t}}^{\mathrm{°}}$t) where t is the transmission matrix. For zero field our expressions reduce to the usual multichannel Landauer formulas. In the absence of dissipation, R approaches zero, t approaches a unit matrix, and quantized values are obtained for the Hall resistance.

I consider learning in neural network models and demonstrate how global properties can be derived from the characteristics of the local synaptic modification rules. I examine, in detail, the case of the Hopfield model of associative memory with Hebbian learning and show how the configuration space is partitioned into orbits of points of equal behavior, yielding a description of the structure of all the stable points. Calculations for a small-sized example are given.

The effects of transverse electric fields on the conductance fluctuations in an Sb loop have been studied. We show that the electric field can be used to tune the position (or phase) of Aharonov-Bohm oscillations as well as to alter the aperiodic conductance fluctuation patterns. We disucss two mechanisms which might cause the observed dependence of the fluctuation pattern on transverse electric field. The first is the electrostatic Aharonov-Bohm effect, and the second is the spatial shifting of the electron trajectories by the electric field.

We show that all the nonrenormalizable terms in the effective superpotential for any Abelian symmetric orbifold with at least (0,2) world-sheet supersymmetry as well as any blown-up (2,2) orbifold are exponentially suppressed by the size R of the compactified space, i.e., ∝exp(-${\mathrm{R}}^2$/α’).

The ratio of an N-point p-loop string amplitude to the N-point tree amplitude is shown to solve Hirota’s bilinear difference equation which is satisfied by all solutions to the Kadomtsev-Petviashvili hierarchy. Evolution of solutions is determined by Koba-Nielsen variables and external momenta. Fay’s trisecant formula emerges as a result.

We partially analyze the two-loop box and hexagon chiral gauge anomalies in D=6 and 10 dimensions for super-Yang-Mills theories. We apply these results to the SO(32) open superstring and show that the leading gauge anomaly vanishes at two-loop order while the subleading gauge anomalies, the mixed anomalies, and the subleading chiral gravitational anomalies may all be canceled with appropriate counterterms. To do this in field theory it is necessary to include a term B(Tr${\mathrm{F}}^2$${)}^2$ which is absent at one-loop order in the zero-slope limit of the SO(32) superstring.

Photoabsorption cross sections of small neutral sodium clusters composed of N=2–40 sodium atoms are measured by longitudinal–beam-depletion spectroscopy at several wavelengths of visible light. Absorption occurs via coupling of photons to collective oscillations of the valence electrons. The cross section is strongly size and wavelength dependent. Good agreement is found with predictions based on an extended Clemenger-Nilsson shell model and the experimental static polarizabilities.

The hydrogen atom in a magnetic field is a classically chaotic Hamiltonian system. The energy-level fluctuations have been shown recently to obey a random-matrix model. Here we go beyond the statistical analysis by studying the destruction of the low-field dynamical symmetries. We especially establish the existence of scars of symmetries in the chaotic regime. The symmetry properties are no longer associated with one given level, but fractalized onto clusters of levels, generating a long-range order.

The first experimental observation of sequential decay of metastable cluster ions is reported herein. Ar cluster ions are produced by electron-impact ionization of a supersonic Ar cluster beam. Some of these ions are observed to decay via sequential decay series in the microsecond time scale, i.e., ${\mathrm{Ar}}_{\mathit{n}}^{+\mathrm{*}}$→${\mathrm{Ar}}_{\mathit{n}\mathrm{-}1}^{+\mathrm{*}}$→${\mathrm{Ar}}_{\mathit{n}\mathrm{-}2}^{+\mathrm{*}}$ (with n≥7), evaporating a single monomer in each of these successive decays. Conversely, the dominant metastable decay of ${\mathrm{Ar}}_4$${\mathrm{}}^{+\mathrm{*}}$→${\mathrm{Ar}}_2$${\mathrm{}}^{+}$ proceeds predominantly via a single-step fissioning process leading to the simultaneous evaporation of two neutral Ar monomers.

The differential formulaton of the Landau-Fokker-Planck collision integral is developed for the case of relativistic electromagnetic interactions.

The whistler electron microinstability has been observed in the Constance B quadrupole-mirror, electron-cyclotron-resonance heated plasma. Experimental evidence indicates that the warm-electron component (2 keV) drives the instability while the hot-electron component (400 keV) is stable. Dispersion-relation calculations using a new distribution function (electron-cyclotron-resonance heated distribution) to model the warm-electron component are in agreement with this experimental result.

A new phenomenon that an ion wave emits an upper-hybrid-wave soliton was observed in a beam-plasma system. Observations were performed by the previously developed time-of-flight method. The necessary phase condition between the ion wave and the upper hybrid soliton was recognized and the growth rate of the upper hybrid wave was obtained experimentally.

We show that the Ising model in three dimensions with a small random magnetic field has two phases at low temperatures, i.e., that its lower critical dimension is at most two. This is shown by our devising an exact renormalization-group flow which takes the theory to the zero-temperature, zero-field fixed point.

Analysis of the results from first-principles calculations produces physical insights to the stability of the missing-row reconstruction on the Au(110) surface. The absence of the missing-row reconstruction on the (110) faces of other fcc metals and the possibility to induce the reconstruction by charge transfer are also explained.

Constant-pressure molecular dynamics has been used to study the mixed crystal (KCl${)}_{0.25}$(KCN${)}_{0.75}$. On cooling from the high-temperature cubic rotator phase, this system undergoes a transition to a ground-state monoclinic structure, with indication of an intermediate rhombohedral phase. At low temperature, the ${\mathrm{CN}}^{\mathrm{-}}$ quadrupoles freeze into a state with disordered orientations, thus suggesting the formation of a noncubic orientational glass phase. The orientational freezing is accompanied by anomalous diffraction profiles.

Phonon dispersion curves of GaAs-AlAs superlattices for various directions of propagation are examined with a detailed microscopic model which takes into account the long-range Coulomb interaction. The anisotropy of the long-wavelength optical modes and its relation with the interface modes are studied. Our theoretical predictions are in accord with the experimental data.

The temperature-dependent dipole-active phonons of the clean c(2×2) W(001) surface, across the reconstruction phase transition at ${\mathrm{T}}_{\mathrm{c}}$≃250 K, are studied by molecular dynamics. Our calculated inelastic electron rate shows a reconstruction-related low-temperature peak, corresponding to a mostly second-layer surface phonon of high frequency. This mode disappears above ${\mathrm{T}}_{\mathrm{c}}$, because of fluctuations of the distortion phase angle, and provides a new explanation of the recent electron-energy-loss spectroscopy data of Woods and Erskine.

The narrow-band noise (NBN) in the charge-density-wave conductor ${\mathrm{NbSe}}_3$ is found to fluctuate dynamically in frequency, amplitude, and harmonic content. The NBN width is dominated by slow frequency fluctuations rather than a spatial velocity distribution. Mode locking quenches these fluctuations yielding a dramatic narrowing of the NBN; but amplitude fluctuations remain. The NBN width also scales with the broad-band noise amplitude. These results demonstrate the crucial importance of temporal incoherence in the sliding charge-density-wave condensate and particularly on mode locking.

A mechanism leading to a temperature-independent dephasing time, ${\tau }_{\phi }$, in the weakly localized regime is discussed. It is shown that the time-reversed complementary scattering paths which lead to weak localization experience a relative phase shift due to the zero-point motion of the ions in the material. By use of a simple model it is shown that this mechanism can explain the saturation of ${\tau }_{\phi }$ which is seen at low temperatures in a wide variety of systems.