On the validity of the Fokker-Planck equation for the Heisenberg magnet

We assume an explicit stochastic dynamics for the microscopic variables in the Heisenberg magnet based on experimental data. We obtain additional terms to the Fokker-Planck Equation and also explicit expressions for the numerical coefficients in the Master Equation, near T_c.     

On the particle excitations in the XXZ spin chain

We continue to study the excited states for the XXZ spin chain corresponding to the complex roots of the Bethe Ansatz equations with the imaginary part equal to π/2$\pi /2$. We propose the particle–hole symmetry which relates the eigenstates build up from the two different pseudovacuum states. We find the XXX spin chain limit for the eigenstates with the complex roots. We also comment on the low-energy excited states for the XXZ spin chain.     

On the polarization of sea antiquarks in the proton

We give some predictions about the magnitude of the sea antiquarks polarization in the proton. In order to get the results we use the experimental data concerning β-decayg _A coupling constants and magnetic moments of octet baryons. We also show the consistency between our calculations and those made in the MIT bag model with one-gluon-exchange correction taken into account. We also quote the numbers for the polarization quantities derived in two specific plausible models.     

On the parameters of the minimal supergravity model

We study systematically the interplay of the parameters of the minimalN=1 supergravity model in a large domain of the parameter space. We make use of the renormalization group equations and the requirement of a correct electroweak symmetry breaking. Particular attention is paid to the dependence on the top mass and the ratio of the two vacuum expectation values, tan β=v ₂/v ₁. We also investigate the mass spectrum of the supersymmetric particles within the allowed parameter range and discuss its relevance for LEP.     

Primordial superstrings and the origin of the universe

We discuss some of the cosmological implications of superstring theories. We pay particular attention to the issue of the initial state and its relationship withR-duality.     

The rise of the cross section and the Mandelstam diagrams

We evaluate multi-pomeron exchanges based on non-planar, Mandelstam-like diagrams of an underlying field theory. We take into account both the coupling of many pomerons to the external lines and the coupling of the pomerons among themselves in a scheme that can incorporate low-energy effects in a natural way. We express the total cross section in terms of one-two-three-pomeron exchange plus a term due to the triple-pomeron interaction. We have considered two possible values for the intercept: α₀ = 1.025, α₀ = 1. In both cases we can find agreement with the observed rise of the pp total cross section.     

Electronic excitations of the rare-gases in the solid phase

We present the results of a simple non-structural approach to the study of the exciton levels in solid rare-gases. We start from the excited states of the free atom and we introduce the solid state effects only through the dielectric constant ?₀ and the effective mass μ. The agreement with the most recent and accurate experimental data is complete for the observed exciton levels in all solid rare-gases. We also provide accurate values for the energy gaps E_g and the effective masses μ.     

Dissipative Evolution of the Qubit State in the Tomographic-Probability Representation

We consider the evolution of qubit states for the Demkov problem in the presence of dephasing processes in the spin tomographic-probability representation. We present an explicit solution of the spin tomogram in terms of the ₁ F ₂ hypergeometric function. We calculate the tomographic Shannon and q entropies through the solution of the master equation in the form of tomographic-probability distribution of the qubit states obtained.     

Cosmic ray constraints on the annihilations of relic particles in the galactic halo

We re-evaluate the fluxes of cosmic ray antiprotons, positrons and gamma rays to be expected from the annihilations of relic particles in the galactic halo. We stress the importance of observational constraints on the possible halo density of relic particles, and specify their annihilation cross sections by the requirement that their cosmological density close the Universe. We use a Monte Carlo programme adapted to fit e⁺e⁻ data to calculate the p̄, e⁺ and γ spectra for some supersymmetric relic candidates. We find significantly smaller p̄ fluxes than previously estimated, and conclude that present upper limits on cosmic ray p̄ and e⁺ do not exclude any range of sparticle masses. We discuss the prospects for possible future constraints on sparticles from cosmic γ rays.     

Computing the Loewner Driving Process of Random Curves in the Half Plane

We simulate several models of random curves in the half plane and numerically compute the stochastic driving processes that produce the curves through the Loewner equation. Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion, as it is for SLE. We find that testing only the normality of the process at a fixed time is not effective at determining if the random curves are an SLE. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N ^1.35) rather than the usual O(N ²), where N is the number of points on the curve.     

On the propagation of a fissioning system across the barrier towards scission

We describe the motion of a fissioning nuclear system from the potential minimum across the saddle region to scission by means of a Fokker-Planck type equation. We pay particular attention to the problems associated with the motion of broad distributions in phase space. We introduce propagators to obtain global solutions. The results are compared with Kramers' stationary solution for all friction and with simplified dynamical calculations which start behind or on top of the barriers. We are able to find stationary solutions numerically for all finite friction values. We compare the corresponding decay rates with Kramers' formulae for large and small friction.     

On the AKSZ Formulation of the Poisson Sigma Model

We review and extend the Alexandrov–Kontsevich–Schwarz–Zaboronsky construction of solutions of the Batalin–Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a special case of this construction yields the Batalin–Vilkovisky action functional of the Poisson sigma model on a disk. As we have shown in a previous paper, the perturbative quantization of this model is related to Kontsevich's deformation quantization of Poisson manifolds and to his formality theorem. We also discuss the action of diffeomorphisms of the target manifolds.     

Quantum Isometries of the Finite Noncommutative Geometry of the Standard Model

We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M × F, where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.     

Duality diagrams and the decays of the ψ and ψ′

We apply duality diagrams to the ψ and ψ′ decays. We propose that the ψ → 3π decay is described by a Virasoro formula, and show that the low mass ππ suppression in ψ′ → ψ2π is a consequence of the threshold factor contained in the Pomeron-2π coupling. We stress the importance of the ψ and ψ′ decays for the study of heavy mesonic resonances.     

QCD corrections to the Drell-Yan mechanism and the pion structure function

We compute the differential cross section dσ/dQ² dy for lepton pair production up to first order in the strong coupling constant α_s. We show that, in the region where the theory applies and where the statistical accuracy of the experiments is good, the ratio of the QCD correction to the Drell-Yan cross section is approximately constant, and that its magnitude is in good agreement with the results of the CERN-NA3 experiment. We thus show that, within the framework of this first-order calculation, the shape of the pion structure function extracted from dilepton production in πp collisions is approximately correct. We also comment on the average transverse momentum of the dilepton due to gluon or quark recoil.     

On the branching structure of the tree of states in spin glasses

We review some known results on the nature of the tree of states in spin glasses and we present new results on its topology. We pay particular attention to the so-called continuum limit in which the levels are labeled by a continuous variablex. We also study the dependence on the levelx of the type of branching (bifurcation, trifurcation,...). We show that the statistics of the tree is universal in the continuum limit, i.e., it does not depend on the details of the algorithm used to generate the tree.     

On the Quantum Invariants for the Spherical Seifert Manifolds

We study the Witten–Reshetikhin–Turaev SU(2) invariant for the Seifert manifolds S ³/Gamma where Γ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that those modular forms have a direct connection with the polyhedral group by showing that the invariant polynomials of modular forms satisfy the polyhedral equations associated to Γ.     

Applicability of the empirical Varshni relation for the temperature dependence of the width of the band gap

We have carried out a comparison of relations used to describe the temperature dependence of the width of the band gap in crystals. It is shown that for kT≫ℏω the well-known Varshni relation can be obtained from the non-empirical Fan expression in explicit form taking account of the phonon statistics. We have calculated the temperature coefficient bof the width of the band gap for a number of materials in the range where the high-temperature condition is not met. We have found that the Varshni relation overestimates β, whereas calculations based on the Fan expression agree with experiment. Fiz. Tverd. Tela (St. Petersburg) 41, 994–998 (June 1999)     

Effect of Tm concentration on the tunability of the YLF laser in the 1.9 µm region

We describe the continuous-wave (cw) operation of a LiYF₄ laser based on crystals doped with different concentrations of Tm³⁺. We observed the fluorescence spectra from the upper laser level when the crystal is placed inside the laser resonator, in the same optical environment of the coherent emission. We measured the laser intensity as a function of pump power and obtained a 24% slope efficiency by selecting a suitable orientation of the crystal. Using all this information, we were able to demonstrate laser tunability at 1.9 µm in a 50 cm^–1 wide interval.