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

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

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

Volatile inventory of Mars-2: Primordial sources and fractionating processes

The total volatile inventory of Mars has been modeled using meteoritic and presumed primordial abundances in the early solar system. Evidence is presented which indicates that the elemental abundances of the noble gases on Earth and Mars are similar, and their ratios are comparable to those in average carbonaceous chondrites with the exception of xenon and krypton. In order to account for presently observed variations in gas abundances, two primordial sources were used. One was the solar composition similar to the solar wind, and the other of carbonaceous grains that were the source for trace exotic components. For Mars, a model in which the early, high solar EUV flux with continued hydrogen production by differentiation results in mass fractionation of the primordial atmosphere, early depletion of xenon, and later depletion of gases lighter than krypton. The result is that the primordial Mars water inventory may have been on the order of 20 to 30 km if spread over the planet