Theory of Nonequilibrium Coherent Transport Through an Interacting Mesoscopic Region Weakly Coupled to Electrodes

We develop a theory for the nonequilibrium coherent transport through a mesoscopic region, based on thenonequilibrium Green function technique. The theory requires the weak coupling bet. ween the central mesoscopic regionand the multiple electrodes, but allows arbitrary hopping and interaction in the central region. An equation determiningthe nonequilibrium distribution in the central interacting region is derived and plays an important role in the theory.The theory is applied to two special cases for demonstrations, revealing the novel effects associated with the combinationof phase coherence, Coulomb interaction, and nonequilibrium distribution.     

Computation of Current Cumulants for Small Nonequilibrium Systems

We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on identifying the current cumulants from a Rayleigh-Schrödinger perturbation expansion for the generating function. Here it is derived from a simple path-distribution identity and extended to the joint statistics of multiple currents. For a possible thermodynamical interpretation, we compare this approach to a generalized Onsager-Machlup formalism. We present calculations for a boundary driven Kawasaki dynamics on a one-dimensional chain, both for attractive and repulsive particle interactions.     

Surface Restructuring, Kinetic Oscillations, and Chaos in Heterogeneous Catalytic Reactions

Kinetic oscillations in catalytic reactions on single-crystal surfaces often result from the interplay of the purely chemical reaction steps and adsorbate-induced surface restructuring. A classical example is CO oxidation on Pt(100). We survey evolution of the models used to simulate this reaction and show how it can be described self-consistently by employing Monte Carlo simulations combined with the lattice-gas model, taking into account substrate-substrate, substrate-adsorbate and adsorbate-adsorbate lateral interactions. Under the reactive conditions, this approach predicts formation of mesoscopic restructured well ordered islands with atomically sharp boundaries.     

Quantum statistics of reaction-diffusion systems

A strictly quantum-statistical theory of inhomogeneous reactions is presented. The treatment is based on the theory of multi-channel reactive scattering. For the configuration probabilities of the reactants a system of reaction-diffusion equations is obtained. The expressions for the diffusion tensor and the reaction-rate coefficients are established in terms of microscopic parameters characteristic of the reacting species.     

Diauxic Growth at the Mesoscopic Scale

In the present paper, we study a diauxic growth that can be generated by a class of model at the mesoscopic scale. Although the diauxic growth can be related to the macroscopic scale, similarly to the logistic scale, one may ask whether models on mesoscopic or microscopic scales may lead to such a behavior. The present paper is the first step towards the developing of the mesoscopic models that lead to a diauxic growth at the macroscopic scale. We propose various nonlinear mesoscopic models conservative or not that lead directly to some diauxic growths.     

Theoretical imaging of current profiles in two-dimensional devices

This paper addresses in a concise and rigorous way the basic tools for the study of local longitudinal and transverse microscopic currents in two-dimensional devices. The emphasis is on the optimized use of the Keldysh nonequilibrium Green's function theory together with the tight-binding representation of the electronic system. We elaborate general analytic expressions of current profiles, useful for modeling and simulating the local site-to-site flow of carriers; furthermore, in broken time-reversal symmetry, the formalism discerns unambiguously persistent and transport contributions to the bond currents. Our approach achieves a workable theoretical imaging, resolved in space and energy, of the microscopic currents through mesoscopic devices.     

Spin-current shot noise as a probe of interactions in mesoscopic systems

It is shown that the spin-resolved current shot noise can probe attractive or repulsive interactions in mesoscopic systems. This is illustrated in two physical situations: (i) a normal-superconducting junction where the spin-current noise is found to be zero, and (ii) a single-electron transistor where the spin-current noise is found to be Poissonian. Repulsive interactions may also lead to weak attractive correlations (bunching of opposite spins) in conditions far from equilibrium. Spin-current shot noise can also be used to measure the spin relaxation time T1, and a setup is proposed in a quantum dot geometry.     

Phase states of multiterminal mesoscopic normal-metal-superconductor structures

We study a mesoscopic normal-metal structure with four superconducting contacts, two of which are joined into a loop. The structure undergoes transitions between three (meta)stable states, with different phase configurations triggered by nonequilibrium conditions. These transitions result in spectacular changes in the magnetoresistance. We find a qualitative agreement between the experiments and a theory based on the quasiclassical Keldysh formalism.     

Nonequilibrium interface equations: An application to thermocapillary motion in binary systems

Interface equations are derived for both binary diffusive and binary fluid systems subjected to nonequilibrium conditions, starting from coarse-grained (mesoscopic) models. The equations are used to describe thermocapillary motion of a droplet in both purely diffusive and fluid cases, and the results are compared with numerical simulations. A mesoscopic chemical potential shift owing to the temperature gradient, and associated mesoscopic corrections involved in droplet motion, are elucidated.     

Stochastic dislocation patterning during cyclic plastic deformation

A dislocation dynamical theory is developed for the formation of dipole dislocation patterns during cyclic plastic deformation in single glide. The stochastic dislocation dynamics adopted is suitable to account, in terms of a fluctuating effective medium, for the effects of long-range dislocation interactions on a mesoscopic scale. The theory can explain the occurrence of a matrix structure and persistent slip bands as a result of evolutionary processes, it gives the intrinsic strain amplitudes and the characteristic wavelength of these structures, and it allows for an interpretation of the structural changes associated with changes of the deformation conditions. Quantitative results are in good agreement with experimental observations.     

Pseudo-spectral methods and linear instabilities in reaction-diffusion fronts

We explore the application of a pseudo-spectral Fourier method to a set of reaction-diffusion equations and compare it with a second-order finite difference method. The prototype cubic autocatalytic reaction-diffusion model as discussed by Gray and Scott [Chem. Eng. Sci. 42, 307 (1987)] with a nonequilibrium constraint is adopted. In a spatial resolution study we find that the phase speeds of one-dimensional finite amplitude waves converge more rapidly for the spectral method than for the finite difference method. Furthermore, in two dimensions the symmetry preserving properties of the spectral method are shown to be superior to those of the finite difference method. In studies of plane/axisymmetric nonlinear waves a symmetry breaking linear instability is shown to occur and is one possible route for the formation of patterns from infinitesimal perturbations to finite amplitude waves in this set of reaction-diffusion equations. (c) 1996 American Institute of Physics.     

Nonequilibrium potential approach: Local and global stability of stationary patterns in an activator-inhibitor system with fast inhibition

We study the formation and global stability of stationary patterns in a finite one-dimensional reaction-diffusion model of the activator-inhibitor type. The analysis proceeds through the study of the nonequilibrium potential or Lyapunov functional for this system considering the fast inhibitor case and, in order to obtain analytical results, the adoption of a piecewise linear version of the model. We have studied the changes in relative stability among the different patterns as the ratio between the diffusion coefficients is varied and have discussed the meaning of the different contributions to the nonequilibrium potential.     

Mathematical Formalism of Nonequilibrium Thermodynamics for Nonlinear Chemical Reaction Systems with General Rate Law

This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with N species, M reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs’ macroscopic chemical thermodynamics under G. N. Lewis’ kinetic law of entire equilibrium (detailed balance in nonlinear chemical kinetics). In doing so, the equilibrium thermodynamics is then naturally generalized to nonequilibrium settings without detailed balance. The kinetic models are represented by a Markovian jumping process. A generalized macroscopic chemical free energy function and its associated balance equation with nonnegative source and sink are the major discoveries. The proof is based on the large deviation principle of this type of Markov processes. A general fluctuation dissipation theorem for stochastic reaction kinetics is also proved. The mathematical theory illustrates how a novel macroscopic dynamic law can emerges from the mesoscopic kinetics in a multi-scale system.     

Derivation and validation of mesoscopic theories for diffusion of interacting molecules

A mesoscopic theory for diffusion of molecules interacting with a long-range potential is derived for Arrhenius microscopic dynamics. Gradient Monte Carlo simulations are presented on a one-dimensional lattice to assess the validity of the mesoscopic theory. Results are compared for Metropolis and Arrhenius microscopic dynamics. Non-Fickian behavior is demonstrated and it is shown that microscopic dynamics dictate the steady-state concentration profiles.     

Nonequilibriurn discontinuous phase transitions in a fast ionic conductor model: Coexistence and spinodal lines

Two-dimensional lattice-gas models with attractive interactions and particle-conserving hopping dynamics under the influence of a very large external electric field along a principal axis are studied in the case of off-critical densities. We describe the corresponding nonequilibrium first-order phase transitions, evaluate coexistence and spinodal lines, and make some comparisons with experimental observations on fast ionic conductors.See Ref. 1 (henceforth referred to as II) for references.     

Pattern formation in the ferrocyanide-iodate-sulfite reaction: the control of space scale separation

We revisit the conditions for the development of reaction-diffusion patterns in the ferrocyanide-iodate-sulfite bistable and oscillatory reaction. This hydrogen ion autoactivated reaction is the only example known to produce sustained stationary lamellar patterns and a wealth of other spatio-temporal phenomena including self-replication and localized oscillatory domain of spots, due to repulsive front interactions and to a parity-breaking front bifurcation (nonequilibrium Ising-Bloch bifurcation). We show experimentally that the space scale separation necessary for the observation of stationary patterns is mediated by the presence of low mobility weak acid functional groups. The presence of such groups was overlooked in the original observations made with hydrolyzable polyacrylamide gels. This missing information made the original observations difficult to reproduce and frustrated further experimental exploitation of the fantastic potentialities of this system. Using one-side-fed spatial reactors filled with agarose gel, we can reproduce all the previous pattern observations, in particular the stationary labyrinthine patterns, by introducing, above a critical concentration, well controlled amounts of polyacrylate chains in the gel network. We use two different geometries of spatial reactors (annular and disk shapes) to provide complementary information on the actual three-dimensional character of spatial patterns. We also reinvestigate the role of other feed parameters and show that the system exhibits both a domain of spatial bistability and of large-amplitude pH oscillations associated in a typical cross-shape diagram. The experimental method presented here can be adapted to produce patterns in the large number of oscillatory and bistable reactions, since the iodate-sulfite-ferrocynide reaction is a prototype of these systems.     

Mesoscopic Modeling for Continuous Spin Lattice Systems: Model Problems and Micromagnetics Applications

In this paper we derive deterministic mesoscopic theories for model continuous spin lattice systems both at equilibrium and non-equilibrium in the presence of thermal fluctuations. The full magnetic Hamiltonian that includes singular integral (dipolar) interactions is also considered at equilibrium. The non-equilibrium microscopic models we consider are relaxation-type dynamics arising in kinetic Monte Carlo or Langevin-type simulations of lattice systems. In this context we also employ the derived mesoscopic models to study the relaxation of such algorithms to equilibrium