Stochastic interacting particle systems out of equilibrium

This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a unified picture is emerging at the macroscopic level, applicable, in our view, to real phenomena where diffusion is the dominating physical mechanism. We rely mainly on an approach developed by the authors based on the study of dynamical large fluctuations in stationary states of open systems. The outcome of this approach is a theory connecting the non equilibrium thermodynamics to the transport coefficients via a variational principle. This leads ultimately to a functional derivative equation of Hamilton-Jacobi type for the non equilibrium free energy in which local thermodynamic variables are the independent arguments. In the first part of the paper we give a detailed introduction to the microscopic dynamics considered, while the second part, devoted to the macroscopic properties, illustrates many consequences of the Hamilton-Jacobi equation. In both parts several novelties are included.Comment: 36 page

Lie groups in nonequilibrium thermodynamics: Geometric structure behind viscoplasticity

Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras. From the characterization of all the Lie groups associated with a given Lie algebra as quotients of a universal covering group, we obtain a natural classification of rheological models based on the concept of discrete reference states and, in particular, we find a clear-cut and deep distinction between viscoplasticity and viscoelasticity. The abstract ideas are illustrated by a naive toy model of crystal viscoplasticity, but similar kinetic models are also used for modeling the viscoplastic behavior of glasses. We discuss some implications for coarse graining and statistical mechanics.Comment: 11 pages, 1 figure, accepted for publication in J. Non-Newtonian Fluid Mech. Keywords: Elastic-viscoplastic materials, Nonequilibrium thermodynamics, GENERIC, Lie groups, Reference state

Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics

We study the flow obtained from a three-layer, eddy-resolving quasigeostrophic ocean circulation model subject to an applied wind stress curl. For this model we will consider transport between the northern and southern gyres separated by an eastward jet. We will focus on the use of techniques from dynamical systems theory, particularly lobe dynamics, in the forming of geometric structures that govern transport. By “govern”, we mean they can be used to compute Lagrangian transport quantities, such as the flux across the jet. We will consider periodic, quasiperiodic, and chaotic velocity fields, and thus assess the effectiveness of dynamical systems techniques in flows with progressively more spatio-temporal complexity. The numerical methods necessary to implement the dynamical systems techniques and the significance of lobe dynamics as a signature of specific “events”, such as rings pinching off from a meandering jet, are also discussed

Ultrafast and reversible control of the exchange interaction in Mott insulators

The strongest interaction between microscopic spins in magnetic materials is the exchange interaction $J_\text{ex}$. Therefore, ultrafast control of $J_\text{ex}$ holds the promise to control spins on ultimately fast timescales. We demonstrate that time-periodic modulation of the electronic structure by electric fields can be used to reversibly control $J_\text{ex}$ on ultrafast timescales in extended antiferromagnetic Mott insulators. In the regime of weak driving strength, we find that $J_\text{ex}$ can be enhanced and reduced for frequencies below and above the Mott gap, respectively. Moreover, for strong driving strength, even the sign of $J_\text{ex}$ can be reversed and we show that this causes time reversal of the associated quantum spin dynamics. These results suggest wide applications, not only to control magnetism in condensed matter systems, for example, via the excitation of spin resonances, but also to assess fundamental questions concerning the reversibility of the quantum many-body dynamics in cold atom systems.Comment: 9 pages, 4 figure

On Time Correlations for KPZ Growth in One Dimension

Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In each case the power laws of the covariance for short and long times are obtained. They are derived from a variational problem involving two independent Airy processes. For stationary initial conditions we derive an exact formula for the stationary covariance with two approaches: (1) the variational problem and (2) deriving the covariance of the time-integrated current at the origin for the corresponding driven lattice gas. In the stationary case we also derive the l arge time behavior for the covariance of the height gradients