Time Averages of Markov Processes and Applications to Two-Timescale Problems

We show a decomposition into the sum of a martingale and a deterministic quantity for time averages of the solutions to non-autonomous SDEs and for discrete-time Markov processes. In the SDE case the martingale has an explicit representation in terms of the gradient of the associated semigroup or transition operator. We show how the results can be used to obtain quenched Gaussian concentration inequalities for time averages and to provide insights into the Averaging principle for two-timescale processes.Comment: 18 page

QCD at high baryon density in a random matrix model

A high density diquark phase seems to be a generic feature of QCD. If so it should also be reproduced by random matrix models. We discuss a specific one in which the random matrix elements of the Dirac operator are supplemented by a finite chemical potential and by non-random elements which model the formation of instanton-anti-instanton molecules. Comparing our results to those found in a previous investigation by Vanderheyden and Jackson we find additional support for our starting assumption, namely that the existence of a high density diquark phase is common to all QCD-like models.Comment: 16 pages, 4 figures, final version to appear in Eur.Phys.J.

The Kondo Lattice Model

In this lecture, we review the experimental situation of heavy Fermions with emphasis on the existence of a quantum phase transition (QPT) and related non-Fermi liquid (NFL) effects. We overview the Kondo lattice model (KLM) which is believed to describe the physics of those systems. After recalling the existing theories based on large-N expansion and various N=2 schemes, we present two alternative approaches: (i) a spin fluctuation-Kondo functional integral approach treating the spin-fluctuation and Kondo effects on an equal footing, and (ii) a supersymmetric theory enlarging the usual fermionic representation of the spin into a mixed fermionic-bosonic representation in order to describe the spin degrees of freedom as well as the Fermi-liquid type excitations. This kind of approaches may open up new prospects for the description of the critical phenomena associated to the quantum phase transition in Heavy-Fermion systems.Comment: 27 pages, 6 figures, 51 references, appeared in the Proceedings of the XXXVIII Cracow School of Theoretical Physics, Zakopane, Poland, June 1-10, 199

Supersymmetric Approach to Heavy-Fermion Systems

We present a new supersymmetric approach to the Kondo lattice model in order to describe simultaneously the quasiparticle excitations and the low-energy magnetic fluctuations in heavy-Fermion systems. This approach mixes the fermionic and the bosonic representation of the spin following the standard rules of superalgebra. Our results show the formation of a bosonic band within the hybridization gap reflecting the spin collective modes. The density of states at the Fermi level is strongly renormalized while the Fermi surface sum rule includes $n_{c}+1$ states. The dynamical susceptibility is made of a Fermi liquid superimposed on a localized magnetism contribution.Comment: 5 pages, 2 figure

Full Service ISDN Satellite (FSIS) network model for advanced ISDN satellite design and experiments

The Full Service Integrated Services Digital Network (FSIS) network model for advanced satellite designs describes a model suitable for discrete event simulations. A top down model design uses the Advanced Communications Technology Satellite (ACTS) as its basis. The ACTS and the Interim Service ISDN Satellite (ISIS) perform ISDN protocol analyses and switching decisions in the terrestrial domain, whereas FSIS makes all its analyses and decisions on-board the ISDN satellite

Scenarios and performance measures for advanced ISDN satellite design and experiments

Described here are the contemplated input and expected output for the Interim Service Integrated Services Digital Network (ISDN) Satellite (ISIS) and Full Service ISDN Satellite (FSIS) Models. The discrete event simulations of these models are presented with specific scenarios that stress ISDN satellite parameters. Performance measure criteria are presented for evaluating the advanced ISDN communication satellite designs of the NASA Satellite Communications Research (SCAR) Program