An Efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. Themethod is based on the Bleher-Its deformation of the model, on its associated integral representation of the free energy, and on a method for solving the string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. As a byproduct we obtain an efficient algorithm to compute generating functions for the enumeration of labeled k-maps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular one-cut models within this approach.

title: Phase structure and critical processes of spectral curves in large N dualities
abstract: We examine the phase structure and the critical processes of the spectral curves that arise in the study of large N dualities between supersymmetric Yang-Mills theories and string models on local Calabi-Yau manifolds. These spectral curves are determined by a set of complex partial 't Hooft parameters and a system of cuts given by projections on the spectral curve of minimal supersymmetric cycles of the underlying Calabi-Yau manifold. Using a combination of analytical and numerical methods we give a complete description of the one-cut phase in the cubic model, determine the analytic condition satisfied by critical one-cut spectral curves, and give an algorithm to calculate the two-cut spectral curves of the cubic model for generic values of the partial 't Hooft parameters.

title: Third-order equation for harmonic generation: complex canonical transformation and JWKB solution
abstract: The quantum description of third harmonic generation can be formulated as an eigenvalue problem for a third-order linear differential equation. We perform a semiclassical study of this third-order equation, generalizing the familiar JWKB theory for the second-order Schrodinger equation, and deriving explicit (albeit approximate) formulas for the eigenvalues within this semiclassical context. A central role in this analysis is played by a nonlinear complex canonical transformation which permits a complete description of the classical motion (generated by a complex polynomial Hamiltonian function) in the complexified position and momentum planes.

title: Third harmonic generation as a third-order quasi-exactly solvable system
abstract: The two degrees of freedom in the usual third harmonic generation effective Hamiltonian can be separated, both classically and quantum mechanically, into a harmonic oscillator and a nonlinear oscillator. In turn, the quantum Hamiltonian of the nonlinear oscillator can be written as a cubic polynomial in the generators of a quasi-exactly solvable Lie algebra, and the physically relevant eigenstates are precisely those that can be determined exactly (although, in general, not explicitly). Since the standard Jeffreys–Wentzel–Kramers–Brillouin methods are not easily applicable to general third-order differential equations, we use a Bohr–Sommerfeld quantization of the classical orbits to obtain approximate explicit formulas for the corresponding quantum eigenvalues.

title: Partition functions and the continuum limit in Penner matrix models
abstract: We present an implementation of the method of orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to determine the coefficients of their perturbative expansions in the continuum limit. The method relies on identities satisfied by the resolvent of the Jacobi matrix in the three-term recursion relation of the associated families of orthogonal polynomials. These identities lead to a convenient formulation of the string equations. As an application, we show that in the continuum limit the free energy of certain exactly solvable models like the linear and double Penner models can be written as a sum of Gaussian contributions plus linear terms. To illustrate the one-cut case we discuss the linear, double and cubic Penner models, and for the two- cut case we discuss theoretically and numerically the existence of a double-branch structure of the free energy for the Gaussian Penner model.

title: Effect of large amplitude fluctuations in the Ginzburg-Landau phase transition
abstract: The lattice Ginzburg-Landau model in d=3 and d=2 is simulated, for different values of the coherence length $\xi$ in units of the lattice spacing $a$, using a Monte Carlo method. The energy, specific heat, vortex density $v$, helicity modulus $\Gamma_\mu$ and mean square amplitude are measured to map the phase diagram on the plane $T-\xi$. When amplitude fluctuations, controlled by the parameter $\xi$, become large ($\xi \sim 1$) a proliferation of vortex excitations occurs changing the phase transition from continuous to first order.

title: Inclusive $\mu$ and $B$ quark production cross-sections in $p\bar{p}$ collisions at $\sqrt{s} = 1.8$ TeV
abstract: We report on a preliminary measurement of the inclusive dimuon cross section in p{bar p} collisions at {radical}s = 1.8 TeV using the D0 detector at the Fermilab Tevatron. From these results, we extract the inclusive b-quark production cross section for the kinematic range {vert_bar}y{sup b}{vert_bar} < 1.0 and 9 GeV/c < p{sub T}{sup b min} < 25 GeV/c. The difference in azimuthal angle in the transverse plane for dimuon pairs from b{bar b} production is also shown.

title: $J/\psi$ production in $p \bar{p}$ collisions at $\sqrt{s}$ = 1.8-TeV
abstract: We have studied J/ψ production in pp collisions at √s = 1.8 TeV with the D∅ detector at Fermilab using μ + μ - data. We have measured the inclusive J/ψ production cross section as a function of J/ψ transverse momentum, p T . For the kinematic range p T > 8 GeV/c and |η| + µ - )= 2.08 ± 0.17(stat) ± 0.46(syst) nb. Using the muon impact parameter we have estimated the fraction of J/ψ mesons coming from B meson decays to be f b = 0.35 ± 0.09(stat)±0.10(syst) and inferred the inclusive b production cross section. From the information on the event topology the fraction of nonisolated J/ψ events has been measured to be fnonisol = 0.64 ± 0.08(stat)±0.06(syst). We have also obtained the fraction of J/ψ events resulting from radiative decays of Χ c states, f Χ = 0.32 ±0.07(stat)±0.07(syst). We discuss the implications of our measurements for charmonium production processes.

title: Color coherence in $p\bar{p}$ collisions at $\sqrt{s} = 1.8$ TeV

title: Search for additional neutral gauge bosons
abstract: We have searched for a heavy neutral gauge boson, Z ′, using the decay channel Z ′ → ee . The data were collected with the DO detector at the Fermilab Tevatron during the 1992–1993 p p collider run at s =1.8 TeV from an integrated luminosity of 15±1 pb −1 . Limits are set on the cross section times brancing ratio for the process p p → Z′ → ee as a function of the Z ′ mass. We exclude the existence of a Z ′ of mass less than 490 GeV/c 2 , assuming a Z ′ with the same coupling strengths to quarks and leptons as the standard model Z boson.