Approach to hyperuniformity of steady states of facilitated exclusion processes.

We consider the fluctuations in the number of particles in a box of sizeLdinZd,d⩾1, in the (infinite volume) translation invariant stationary states of the facilitated exclusion process, also called the conserved lattice gas model. When started in a Bernoulli (product) measure at densityρ, these systems approach, ast→∞, a 'frozen' state forρ⩽ρc, withρc=1/2ford = 1 andρc<1/2ford⩾2. Atρ=ρcthe limiting state is, as observed by Hexner and Levine, hyperuniform, that is, the variance of the number of particles in the box grows slower thanLd. We give a general description of how the variances at different scales ofLbehave asρ↗ρc. On the largest scale,L≫L2, the fluctuations are normal (in fact the same as in the original product measure), while in a regionL1≪L≪L2, with bothL1andL2going to infinity asρ↗ρc, the variance grows faster than normal. For1≪L≪L1the variance is the same as in the hyperuniform system. (All results discussed are rigorous ford = 1 and based on simulations ford⩾2.).

Kardar-Parisi-Zhang universality class and the anchored Toom interface.

We revisit the anchored Toom interface and use Kardar-Parisi-Zhang scaling theory to argue that the interface fluctuations are governed by the Airy1 process with the role of space and time interchanged. The predictions, which contain no free parameter, are numerically well confirmed for space-time statistics in the stationary state. In particular, the spatial fluctuations of the interface computed numerically agree well with those given by the GOE edge distribution of Tracy and Widom [Commun. Math. Phys. 177, 727 (1996)].

Nonequilibrium stationary state of a harmonic crystal with alternating masses.

We analyze the nonequilibrium steady states (NESS) of a one-dimensional harmonic chain of N atoms with alternating masses connected to heat reservoirs at unequal temperatures. We find that the temperature profile defined through the local kinetic energy T(j)≡/mj oscillates with period two in the bulk of the system. Depending on boundary conditions, either the heavier or the lighter particles in the bulk are hotter. We obtain explicit integral expressions for the bulk temperature profile and steady state current in the limit N→∞. These depend on whether N is odd or even. We also study similar temperature oscillations in the NESS of systems with noise in the dynamics. These die out as N→∞.

Heat conduction in disordered harmonic lattices with energy-conserving noise.

We study heat conduction in a harmonic crystal whose bulk dynamics is supplemented by random reversals (flips) of the velocity of each particle at a rate λ. The system is maintained in a nonequilibrium stationary state (NESS) by contacts with white-noise Langevin reservoirs at different temperatures. We show that the one-body and pair correlations in this system are the same (after an appropriate mapping of parameters) as those obtained for a model with self-consistent reservoirs. This is true both for the case of equal and random (quenched) masses. While the heat conductivity in the NESS of the ordered system is known explicitly, much less is known about the random mass case. Here we investigate the random system with velocity flips. We improve the bounds on the Green-Kubo conductivity obtained by Bernardin [J. Stat. Phys. 133, 417 (2008)]. The conductivity of the one-dimensional system is then studied both numerically and analytically. This sheds some light on the effect of noise on the transport properties of systems with localized states caused by quenched disorder.

Effect of phonon-phonon interactions on localization.

We study the heat current J in a classical one-dimensional disordered chain with on-site pinning and with ends connected to stochastic thermal reservoirs at different temperatures. In the absence of anharmonicity all modes are localized and there is a gap in the spectrum. Consequently J decays exponentially with system size N. Using simulations we find that even a small amount of anharmonicity leads to a J approximately 1/N dependence, implying diffusive transport of energy.

Boltzmann entropy for dense fluids not in local equilibrium.

Using computer simulations, we investigate the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables M describing the system are the (empirical) particle density f=[f(x,v)] and the total energy E. We find that S(f(t),E) is a monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of S(M(t))=S(M(X(t))) should hold generally for "typical" (the overwhelming majority of) initial microstates (phase points) X0 belonging to the initial macrostate M0, satisfying M(X0)=M(0). This is a consequence of Liouville's theorem when M(t) evolves according to an autonomous deterministic law.

Space-charge-limited 2D electron flow between two flat electrodes in a strong magnetic field.

An approximate analytic solution is constructed for the 2D space-charge-limited emission by a cathode surrounded by nonemitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic problem in vacuum is matched to the solution of a linearized problem in the space charge region whose boundaries are sharp due to the presence of a strong magnetic field. The current density growth in a narrow interval near the edges of the cathode depends strongly on Lambda. We obtain an empirical formula for the total current as a function of Lambda which extends to more general cathode geometries.

Exact free energy functional for a driven diffusive open stationary nonequilibrium system.

We obtain the exact probability exp[-LF([rho(x)])] of finding a macroscopic density profile rho(x) in the stationary nonequilibrium state of an open driven diffusive system, when the size of the system L-->infinity. F, which plays the role of a nonequilibrium free energy, has a very different structure from that found in the purely diffusive case. As there, F is nonlocal, but the shocks and dynamic phase transitions of the driven system are reflected in nonconvexity of F, in discontinuities in its second derivatives, and in non-Gaussian fluctuations in the steady state.

Properties of stationary nonequilibrium states in the thermostatted periodic Lorentz gas: the multiparticle system.

We study the stationary nonequilibrium states of N-point particles moving under the influence of an electric field E among fixed obstacles (disk) in a two-dimensional torus. The total kinetic energy of the system is kept constant through a Gaussian thermostat that produces a velocity dependent mean field interaction between the particles. The current and the particle distribution functions are obtained numerically and compared for small /E/ with analytic solutions of a Boltzmann-type equation obtained by treating the collisions with the obstacles as random independent scatterings. The agreement is surprisingly good for both small and large N. The latter system in turn agrees with a self-consistent one-particle evolution expected to hold in the N-->infinity limit.

Thermodynamic entropy production fluctuation in a two-dimensional shear flow model.

We investigate fluctuations in the momentum flux across a surface perpendicular to the velocity gradient in a stationary shear flow maintained by either thermostated deterministic or by stochastic boundary conditions. In the deterministic system the fluctuation relation for the probability of large deviations, which holds for the phase space volume contraction giving the Gibbs ensemble entropy production, never seems to hold for the flux which gives the hydrodynamic entropy production. In the stochastic case the fluctuation relation is found to hold for the total flux, as predicted by various exact results, but not for the flux across part of the surface. The latter appear to satisfy a modified fluctuation relation. Similar results are obtained for the heat flux in a steady state produced by stochastic boundaries at different temperatures.

Free energy functional for nonequilibrium systems: an exactly solvable case.

We consider the steady state of an open system in which there is a flux of matter between two reservoirs at different chemical potentials. For a large system of size N, the probability of any macroscopic density profile rho(x) is exp[-NF([rho])]; F thus generalizes to nonequilibrium systems the notion of free energy density for equilibrium systems. Our exact expression for F is a nonlocal functional of rho, which yields the macroscopically long range correlations in the nonequilibrium steady state previously predicted by fluctuating hydrodynamics and observed experimentally.

Surface-directed spinodal decomposition in binary fluid mixtures.

We consider the phase separation of binary fluids in contact with a surface, which is preferentially wetted by one of the components of the mixture. We review the results available for this problem and present numerical results obtained using a mesoscopic level simulation technique for the three-dimensional problem.

Remark on the (non)convergence of ensemble densities in dynamical systems.

We consider a dynamical system with state space M, a smooth, compact subset of some R(n), and evolution given by T(t), x(t)=T(t)x, x in M; T(t) is invertible and the time t may be discrete, t in Z, T(t)=T(t), or continuous, t in R. Here we show that starting with a continuous positive initial probability density rho(x,0)>0, with respect to dx, the smooth volume measure induced on M by Lebesgue measure on R(n), the expectation value of logrho(x,t), with respect to any stationary (i.e., time invariant) measure nu(dx), is linear in t, nu(logrho(x,t))=nu(logrho(x,0))+Kt. K depends only on nu and vanishes when nu is absolutely continuous with respect to dx.(c) 1998 American Institute of Physics.

(Global and local) fluctuations of phase space contraction in deterministic stationary nonequilibrium.

We studied numerically the validity of the fluctuation relation introduced in Evans et al. [Phys. Rev. Lett. 71, 2401-2404 (1993)] and proved under suitable conditions by Gallavotti and Cohen [J. Stat. Phys. 80, 931-970 (1995)] for a two-dimensional system of particles maintained in a steady shear flow by Maxwell demon boundary conditions [Chernov and Lebowitz, J. Stat. Phys. 86, 953-990 (1997)]. The theorem was found to hold if one considers the total phase space contraction sigma occurring at collisions with both walls: sigma=sigma( upward arrow )+sigma( downward arrow ). An attempt to extend it to more local quantities sigma( upward arrow ) and sigma( downward arrow ), corresponding to the collisions with the top or bottom wall only, gave negative results. The time decay of the correlations in sigma( upward arrow, downward arrow ) was very slow compared to that of sigma. (c) 1998 American Institute of Physics.

Spectral and stability aspects of quantum chaos.

The relation between the spectrum of a generalized quasienergy operator and the stability of quantum systems driven by quasiperiodic time-dependent forces is discussed.

Saliva from patients with cystic fibrosis inhibits amiloride-sensitive sodium transport.

A factor is present in the saliva and sweat from patients with cystic fibrosis (CF) which inhibits the reabsorption of sodium in the ducts of the salivary and sweat glands. Inasmuch as the physiology of sodium absorption is similar in salivary ducts and the distal colon, we have examined the sensitivity of the sodium absorption in the rat colon to saliva from CF patients. Sodium absorption by the rat colon, estimated as the shortcircuit current, was inhibited by saliva from both patients with CF and normal volunteers. However, only with CF saliva was the inhibition consistently proportional to the saliva concentration. Furthermore, the inhibitory activity of CF saliva was greater than the inhibition observed with saliva from age- and sex-matched controls (percentage of inhibition: CF = 20.1 +/- 2.2, and controls = 14.9 +/- 2.1; P < 0.02), and the inhibition of the colonic shortcircuit current was proportional to the activity measured by the ductal retrograde perfusion assay with the rat parotid gland (linear correlation coefficient = 0.634; P < 0.005). This latter assay is an accepted assay for CF factor activity. We conclude that the CF factor present in saliva probably interacts in a reversible manner with the amiloride-sensitive sodium transport system which is present in all sodium scavenging epithelia. The rat colon is a promising assay system for CF factor activity because the electrical measurements permit a rapid quantitative estimate of activity and a single piece of tissue can be used to measure the activity of several saliva samples.