An exact solution is presented of the Fokker-Planck equation which governs the evolution of an ensemble of disordered metal wires of increasing length, in a magnetic field. By a mapping onto a free-fermion problem, the complete probability distribution function of the transmission eigenvalues is obtained. The logarithmic eigenvalue repulsion of random-matrix theory is shown to break down for transmission eigenvalues which are not close to unity.

Mesoscopic fluctuations in the transport properties of quasi-one-dimensional conductors are studied via the eigenvalue distribution of the transmission matrix. Fluctuations in the universal regime are characterized completely by the two-point correlation function of the eigenvlaue density at scales large compared to the mean eigenvalue spacing. This correlation function is calculated exactly.

We consider the integer quantum Hall effect on a square lattice in a uniform rational magnetic field. The relation between two different interpretations of the Hall conductance as topological invariants is clarified. One is the Thouless–Kohmoto–Nightingale–den Nijs (TKNN) integer in the infinite system and the other is a winding number of the edge state. In the TKNN form of the Hall conductance, a phase of the Bloch wave function defines U(1) vortices on the magnetic Brillouin zone and the total vorticity gives ${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}$. We find that these vortices are given by the edge states when they are degenerate with the bulk states.

We introduce a solvable model of a one-dimensional electron gas interacting with an array of dynamical scattering centers, whose state is specified by a pseudospin variable. In the dilute limit, for frequencies ω and temperatures T below the single-center Kondo scale but above a coherence scale Δ, the physics is governed by the fixed point of the single-impurity two-channel Kondo problem, and the physical properties are reminiscent of the normal state of the high-temperature superconductors. As ω and T→0, three susceptibilities are equally divergent: (1) conventional, spin-singlet even-parity pairing, (2) composite spin-singlet odd-parity pairing, and (3) odd-parity pseudospin.

We calculate the microwave conductivity of a ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ superconductor in the presence of elastic impurity scattering and inelastic scattering due to antiferromagnetic spin fluctuations. The low-temperature conductivity does not simply reflect the linear temperature dependence of the number of quasiparticles in a d-wave system, as often supposed. We compare with recent data on high-quality ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.95}$ single crystals.

We have observed electric-dipole-forbidden electronic excitations with ${\mathit{A}}_{2\mathit{g}}$, ${\mathit{B}}_{1\mathit{g}}$, and ${\mathit{A}}_{1\mathit{g}}$ symmetries at energies near the charge-transfer gap in insulating cuprates, using large-shift Raman techniques. The strongest feature, with pseudovector ${\mathit{A}}_{2\mathit{g}}$ symmetry, occurs in insulating cuprates just below the main optical absorption peak, varying from 0.15 to 0.2 eV below according to the Cu coordination number. ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$ spectra at different doping levels show that all the new features are suppressed in metallic phases. We propose two possible interpretations: internal ${\mathit{d}}^{9\mathrm{-}}$${\mathit{d}}^9$ and charge-transfer ${\mathit{d}}^{9\mathrm{-}}$${\mathit{d}}^{10}$L excitations.

Numerical simulations of a driven elastic string in a quenched random potential at finite temperatures support the existence of glassy motion for sufficiently weak driving forces. Avalanchelike string motion is observed in the transition region.

We have directly measured the transport of heavy-hole excitons in a type-II GaAs/AlAs superlattice. Our results constitute the first direct confirmation of exciton localization in type-II structures and thermal activation to more mobile states. We have also developed a quantitative model to explain our transport and kinetics results, and have obtained the nonradiative interfacial defect density.

We present C 1s autoionization studies of condensed and Xe matrix-isolated ${\mathrm{C}}_{60}$ molecules which give direct information on electron hopping rates in solid ${\mathrm{C}}_{60}$ in the presence of a C 1s vacancy. These rates vary dramatically for the first three C 1s absorption excitation maxima in a pattern consistent with strong electron-electron correlations. Hopping associated with the second excited state involves extramolecular screening comparable to the Mott-Hubbard pseudogap predicted for ${\mathrm{K}}_3$${\mathrm{C}}_{60}$, suggesting intramolecular correlations do not dominate electron transport in the alkali fullerides.

The C 1s exciton in diamond is studied by soft x-ray emission excited with high resolution monochromatic photons. A strong phonon sideband of 5 eV wide is observed in the exciton recombination spectrum. With the phonon contribution, the exciton binding energy is estimated to be 1.5 eV. The excited atoms is suggested to undergo Jahn-Teller relaxation similar to that of the nitrogen impurities in diamond. A similar exciton is observed at the ${\mathrm{\sigma }}^{\mathrm{*}}$-band threshold in graphite. These results provide new insights to the understanding of the core exciton and the donor problem in diamond and other systems.

The dynamics of a class of aggregation models proposed by Takayasu and co-workers are solved exactly in one dimension and in the mean field limit. These models describe the aggregation of positive and negative charges. In one dimension, we find the dynamical cluster-size exponents z=3/2 and ${\mathit{z}}_{\mathit{c}}$=3/4 when the average flux of injected charges is nonzero and zero, respectively. We also find the crossover exponent near the transition to be φ=4/3. Within mean field theory, we find these exponents to be z=2, ${\mathit{z}}_{\mathit{c}}$=1, and φ=1. Assuming dynamic scaling, we show that in any dimension, these exponents are related to one single static exponent.

We study the diffusion-limited reactions 3A→2A and 3A→A in one dimension. The analytic method of interparticle distribution functions is extended to the case where lattice sites can be occupied by more than one particle. The exact leading time behavior of the concentration decay, and the distribution of distances between nearest particles in the long time asymptotic limit are computed. Results of extensive numerical simulations are also presented. From the numerical data, we observe the previously postulated logarithmic corrections to the concentration power-law decay.

The quantum statistics of charged, extremal black holes is investigated beginning with the hypothesis that the quantum state is a functional on the space of closed three-geometries, with each black hole connected to an oppositely charged black hole through a spatial wormhole. From this starting point a simple argument is given that a collection of extremal black holes obeys neither Bose nor Fermi statistics. Rather, they obey an exotic variety of particle statistics known as ‘‘infinite statistics’’ which resembles that of distinguishable particles and is realized by a q deformation of the quantum commutation relations.

The Utah Fly’s Eye detector has revealed a change in the cosmic ray composition which is correlated with structure in the all-particle energy spectrum. The data can be fitted by a simple model of a steep power law spectrum of heavy nuclei which is overtaken at high energies by a flatter spectrum of protons. The transition occurs near ${10}^{18.5}$ eV. Anisotropy is not detected, so the high-rigidity particles above the transition energy do not originate in the disk of the Galaxy. An outstanding event of 3×${10}^{20}$ eV implies that the highest energy particles originate in the contemporary era of the Universe.

We propose a simple model for a free relativistic particle of fractional spin in 2+1 dimensions. Using the Hamiltonian formulation with the set of constraints, we introduce the electromagnetic interaction of a charged anyon and obtain the Lagrangian. The Casimir operator of the extended algebra, which is the first-class constraint, is obtained and gives the equation of motion of the anyon. In particular, from the latter it follows that the gyromagnetic ratio for a charged anyon is two due to the parallelness of spin and momentum of the particle in 2+1 dimensions. The canonical quantization is also considered.

We consider the c=1 matrix model deformed by the operator 1/2M Tr${\mathrm{\Phi }}^{\mathrm{-}2}$, which was conjectured by Jevicki and Yoneya to describe a two-dimensional black hole of mass M. We calculate the exact nonperturbative S matrix and show that all the amplitudes involving an odd number of particles vanish at least to all orders of perturbation theory. We conjecture that these amplitudes vanish nonperturbatively and prove this for the 2n→1 scattering. For the two- and four-particle amplitudes we give some leading terms of the perturbative expansion.

We present a reliable estimate on the production rate of ${\mathit{B}}_{\mathit{c}}$ mesons in 1S and 2S states in the large transverse momentum region at hadron colliders using heavy quark fragmentation functions derived within the framework of perturbative QCD. We also present the transverse momentum distribution for the ${\mathit{B}}_{\mathit{c}}$ mesons. The production rate is large enough for the ${\mathit{B}}_{\mathit{c}}$ mesons to be identified at the Fermilab Tevatron. At the Superconducting Super Collider or the CERN Large Hadron Collider the rate is so large that their properties can be studied in detail.

We have measured the magnetic moments of the ${\mathrm{\Sigma }}^{+}$ and Σ¯ ${}_{}{}^{\mathrm{-}}{}_{}{}^{}$ hyperons produced by 800-GeV protons incident on a Cu target. We determine the ${\mathrm{\Sigma }}^{+}$ magnetic moment to be (2.4613±0.0034±0.0040)${\mathrm{\mu }}_{\mathit{N}}$ where the uncertainties are statistical and systematic, respectively. In this first measurement we determine the magnetic moment of the Σ¯ ${}_{}{}^{\mathrm{-}}{}_{}{}^{}$ to be -(2.428±0.036±0.007)${\mathrm{\mu }}_{\mathit{N}}$. The magnetic moments of the ${\mathrm{\Sigma }}^{+}$ and Σ¯ ${}_{}{}^{\mathrm{-}}{}_{}{}^{}$ are consistent with each other in magnitude but opposite in sign as required by CPT invariance.

The average b-hadron lifetime has been measured using a high statistics sample of B→J/ψ X decays recorded with the Collider Detector at Fermilab. The decay vertices of 5344 inclusive J/ψ→${\mathrm{\mu }}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$ candidates have been reconstructed using information from a silicon vertex detector. The measured B lifetime, which is the average over all b hadrons produced in pp¯ collisions at √s =1.8 TeV weighted by their branching ratios into J/ψ, is 1.46±0.06(stat)±0.06(syst) ps.

We report an experimental demonstration of diffraction of ${\mathrm{He}}^{\mathrm{*}}$ atoms from a magneto-optical grating. The grating was produced by the interaction of three-level atoms with a light field of spatially varying polarization and a magnetic field. For a light shift matched to the Zeeman shift, a two-peaked diffraction pattern was observed, corresponding to a momentum splitting of 42ħk. The effect of changing the polarizations of the light field was investigated. The diffraction from the magneto-optical grating is compared directly with the diffraction of two-level atoms from a standing light wave and it is shown, that the magneto-optical interaction leads to more efficient coupling into high order momentum states.