Symmetric Simple Exclusion Process:¶Regularity of the Self-Diffusion Coefficient

We prove that the self-diffusion coefficient of a tagged particle in the symmetric exclusion process in Z ^d , which is in equilibrium at density α, is of class C ^∞ as a function of α in the closed interval [0,1]. The proof provides also a recursive method to compute the Taylor expansion at the boundaries. Received: 6 December 2000 / Accepted: 6 April 2001     

On the sector condition and homogenization of diffusions with a Gaussian drift

In this paper we present the functional central limit theorem for a class of Markov processes, whose L²-generator satisfies the so-called graded sector condition. We apply the result to obtain homogenization theorems for certain classes of diffusions with a random Gaussian drift. Additionally, we present a result concerning the regularity of the effective diffusivity tensor with respect to the parameters related to the statistics of the drift. The abstract central limit theorem, see Theorem 2.2, is obtained by applying the technique used in Sethuraman et al. (Comm. Pure Appl. Math. 53 (2000) 972) to the case of infinite particle systems.     

Derivation of Cahn-Hilliard equations from Ginzburg-Landau models

The generalized Cahn-Hilliard equation is obtained as the hydrodynamic limit from a stochastic Ginzburg-Landau model. The associated large-deviation principle is also proved. In the one-dimensional case, we prove a related result about the scaling limit of conservative Langevin dynamics of an SOS surface.     

Hydrodynamics and large deviation for simple exclusion processes

We prove the hydrodynamical limit for weakly asymmetric simple exclusion processes. A large deviation property with respect to this limit is established for the symmetric case. We treat also the situation where a slow reaction (creation and annihilation of particles) is present.     

Synthesis,Spectral, Valence‐Bond Parameters,and Single Crystal X‐ray Structural Studies on [Ni(dnpdtc)(PPh3)(NCS)] and [Ni(dnpdtc)(PPh3)(CN)]

Two new nickel complexes withplanar surrounding of Ni [Ni(dnpdtc)(PPh₃)(NCS)] (1) and [Ni(dnpdtc)(PPh₃)(CN)] (2) (dnpdtc=N, N‐dipropyldithiocarbamate) were prepared from the parent dithiocarbamate and were characterized by elemental analysis, electronic, IR and NMR spectra. The structures of both the complexes were determined by single crystal X‐ray crystallography. Thioureide stretching vibrations occur at 1528 cm^‐1 and 1521 cm^‐1 for 1 and 2 respectively. Large ³¹P chemical shifts were observed for the two compounds. A significant asymmetry in Ni—S bond distances was observed in compound 1 [2.1700(16) and 2.2251(17)Å] whereas in compound 2 the bond distances were almost similar [2.2100(14) and 2.2122(13)Å]. A marginal difference was observed with respect to the thioureide bond distances [1.340(6)Å for 1 and 1.312(5)Å for 2 ]. The observation clearly supports the less effective trans influence of SCN^— over PPh₃. However, PPh₃ and CN^— show almost similar trans influence.     

Anomalous transport and relaxation in classical one-dimensional models

After reviewing the main features of anomalous energy transport in 1D systems, we report simulations performed with chains of noisy anharmonic oscillators. The stochastic terms are added in such a way to conserve total energy and momentum, thus keeping the basic hydrodynamic features of these models. The addition of this “conservative noise" allows to obtain a more efficient estimate of the power-law divergence of heat conductivity κ(L) ∼L^α in the limit of small noise and large system size L. By comparing the numerical results with rigorous predictions obtained for the harmonic chain, we show how finite-size and time effects can be effectively controlled. For low noise amplitudes, the α values are close to 1/3 for asymmetric potentials and to 0.4 for symmetric ones. These results support the previously conjectured two-universality-classes scenario.     

Hydrodynamic Limit for a Hamiltonian System with Boundary Conditions and Conservative Noise

We study the hyperbolic scaling limit for a chain of N coupled anharmonic oscillators. The chain is attached to a point on the left and there is a force (tension) τ acting on the right. In order to provide good ergodic properties to the system, we perturb the Hamiltonian dynamics with random local exchanges of velocities between the particles, so that momentum and energy are locally conserved. We prove that in the macroscopic limit the distributions of the elongation, momentum and energy converge to the solution of the Euler system of equations in the smooth regime.     

Heat Conduction and Entropy Production in Anharmonic Crystals with Self-Consistent Stochastic Reservoirs

We investigate a class of anharmonic crystals in d dimensions, d≥1, coupled to both external and internal heat baths of the Ornstein-Uhlenbeck type. The external heat baths, applied at the boundaries in the 1-direction, are at specified, unequal, temperatures T _l and T _r . The temperatures of the internal baths are determined in a self-consistent way by the requirement that there be no net energy exchange with the system in the non-equilibrium stationary state (NESS). We prove the existence of such a stationary self-consistent profile of temperatures for a finite system and show that it minimizes the entropy production to leading order in (T _l ?T _r ). In the NESS the heat conductivity κ is defined as the heat flux per unit area divided by the length of the system and (T _l ?T _r ). In the limit when the temperatures of the external reservoirs go to the same temperature T, κ(T) is given by the Green-Kubo formula, evaluated in an equilibrium system coupled to reservoirs all having the temperature T. This κ(T) remains bounded as the size of the system goes to infinity. We also show that the corresponding infinite system Green-Kubo formula yields a finite result. Stronger results are obtained under the assumption that the self-consistent profile remains bounded.     

Momentum conserving model with anomalous thermal conductivity in low dimensional systems

Anomalous large thermal conductivity has been observed numerically and experimentally in one- and two-dimensional systems. There is an open debate about the role of conservation of momentum. We introduce a model whose thermal conductivity diverges in dimensions 1 and 2 if momentum is conserved, while it remains finite in dimension d > or = 3. We consider a system of harmonic oscillators perturbed by a nonlinear stochastic dynamics conserving momentum and energy. We compute explicitly the time correlation function of the energy current C(J)(t), and we find that it behaves, for large time, like t(-d/2) in the unpinned cases, and like t(-d/2-1) when an on-site harmonic potential is present. This result clarifies the role of conservation of momentum in the anomalous thermal conductivity in low dimensions.     

Large deviation for stationary processes

A quasi-local variational characterization of the entropy for stationary processes is given. This is used to establish upper and lower large deviation estimates for arbitrary stationary processes. The upper and lower rate functions are shown to coincide for all quasi-local stationary processes. The contents of the paper is the following: 1. Introduction; 2. Notations; 3. Relative entropy of conditional expectations; 4. Relative entropy of a stationary process with respect to a covariant family of conditional expectations; 5. The role of locality and quasi-locality properties; 6. Large deviation upper estimate; 7. The Lower estimate; 8. The variational principle.