Almost-Sure Central Limit Theorem for Directed Polymers and Random Corrections

We consider a general model of directed polymers on the lattice , weakly coupled to a random environment. We prove that the central limit theorem holds almost surely for the discrete time random walk X _T associated to the polymer. Moreover we show that the random corrections to the cumulants of X _T are finite, starting from some dimension depending on the index of the cumulants, and that there are corresponding random corrections of order , , in the asymptotic expansion of the expectations of smooth functions of X _T . Full proofs are carried out for the first two cumulants. We finally prove a kind of local theorem showing that the ratio of the probabilities of the events to the corresponding probabilities with no randomness, in the region of “moderate” deviations from the average drift bT, are, for almost all choices of the environment, uniformly close, as , to a functional of the environment “as seen from (T,y)$”. Received: 14 October 1996 / Accepted: 28 March 1997     

Diffusive behavior of asymmetric zero-range processes

We investigate a new interpretation for the Navier-Stokes corrections to the hydrodynamic equation of asymmetric interacting particle systems. We consider a system that starts from a measure associated with a profile that is constant along the drift direction. We show that under diffusive scaling the macroscopic behavior of the process is described by a nonlinear parabolic equation whose diffusion coefficient coincides with the diffusion coefficient of the hydrodynamic equation of the symmetric version of the process.     

Heavy Majorana neutrinos in e + e − → W + W−

In this paper we investigate the effects of heavy Majorana neutrinos in the reaction e ⁺ e ^? → W ⁺ W ^?. We consider neutrino masses in the 1–10 TeV region. We show that at LEP II and NLC energies it is possible to use this processes to verify indirect evidence of heavy neutral particles with mixing angles of the order sin² α = 0.01. We discuss the unitarity restrictions that can be obtained for vector singlet and fermion-mirror-fermion models.     

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997     

Open Problems

Periodica Mathematica Hungarica -     

Rarefied Flow Computations Using Nonlinear Model Boltzmann Equations

High resolution finite difference schemes for solving the nonlinear model Boltzmann equations are presented for the computations of rarefied gas flows. The discrete ordinate method is first applied to remove the velocity space dependency of the distribution function which renders the model Boltzmann equation in phase space to a set of hyperbolic conservation laws with source terms in physical space. Then a high order essentially nonoscillatory method due to Harten et al. (J. Comput. Phys. 71, 231, 1987) is adapted and extended to solve them. Explicit methods using operator splitting and implicit methods using the lower-upper factorization are described to treat multidimensional problems. The methods are tested for both steady and unsteady rarefied gas flows to illustrate its potential use. The computed results using model Boltzmann equations are found to compare well both with those using the direct simulation Monte Carlo results in the transitional regime flows and those with the continuum Navier-Stokes calculations in near continuum regime flows.     

Relativistic quantum defect calculations on the copper isoelectronic sequence

The quantum defect orbital (QDO ) method and its relativistic (RQDO ) counterpart have been employed in this work to compute oscillator strengths for several fine-structure transitions in members of the copper isoelectronic sequence up to Z = 92. The RQDO results are found to be in quite good agreement with the best estimates derived from other sources, whenever the comparison is possible. © 1994 John Wiley & Sons, Inc.