Generalized Exclusion Processes: Transport Coefficients

A class of generalized exclusion processes parametrized by the maximal occupancy, $k\geq 1$, is investigated. For these processes with symmetric nearest-neighbor hopping, we compute the diffusion coefficient and show that it is independent on the spatial dimension. In the extreme cases of $k=1$ (simple symmetric exclusion process) and $k=\infty$ (non-interacting symmetric random walks) the diffusion coefficient is constant; for $2\leq k<\infty$, the diffusion coefficient depends on the density and the maximal occupancy $k$. We also study the evolution of a tagged particle. It exhibits a diffusive behavior which is characterized by the coefficient of self-diffusion which we probe numerically.Comment: v1: 9 pages, 6 figures. v2: + 2 references. v3: 10 pages, 7 figures, published versio

Stochastic exclusion processes versus coherent transport

Stochastic exclusion processes play an integral role in the physics of non-equilibrium statistical mechanics. These models are Markovian processes, described by a classical master equation. In this paper a quantum mechanical version of a stochastic hopping process in one dimension is formulated in terms of a quantum master equation. This allows the investigation of coherent and stochastic evolution in the same formal framework. The focus lies on the non-equilibrium steady state. Two stochastic model systems are considered, the totally asymmetric exclusion process and the fully symmetric exclusion process. The steady state transport properties of these models is compared to the case with additional coherent evolution, generated by the $XX$-Hamiltonian

Collision number statistics for transport processes

Many physical observables can be represented as a particle spending some random time within a given domain. For a broad class of transport-dominated processes, we detail how it is possible to express the moments of the number of particle collisions in an arbitrary volume in terms of repeated convolutions of the ensemble equilibrium distribution. This approach is shown to generalize the celebrated Kac formula for the moments of residence times, which is recovered in the diffusion limit. Some practical applications are illustrated for bounded, unbounded and absorbing domains.Comment: 4 pages, 4 figure

Transport and Reaction Processes in Soil

In order to register agrochemicals in Europe it is necessary to have a detailed understanding of the processes in the environment that break down agrochemicals. The existing framework for environmental assessment includes a consideration of soil water movement and microbial breakdown of products in soil and these processes are relatively understood and represented in models. However the breakdown of agrochemicals by the action of light incident on the soil surface by a process termed photolysis is not so well represented in models of environmental fate. The problem brought by Syngenta (one of the worlds leading agrochemical companies) to the workshop was how to include the effects of light degradation of chemicals into predictive models of environmental fate. Photolysis is known to occur in a very thin layer at the surface of soil. The workshop was asked to consider how the very rough nature of the upper surface of a ploughed field might affect the degradation of chemicals by sunlight. The discussions were directed down two avenues: - firstly to determine how the very small distances over which photolysis occurs might be adequately incorporated into models of transport in soils and, - secondly to consider how the rough surface might modify the illumination of the surface and hence alter degradation. The rate of degradation by photolysis is measured in the laboratory by illuminating a thin, typically about 1 or 2 mm, layer of soil with very strong xenon lamps. The amount of chemical is measured at various intervals and is fitted to a first-order process. Field experiments where the chemical is sprayed on a bare field show evidence of photolysis indicated by biphasic degradation patterns and the presence of breakdown products only formed by photolysis. This report addresses methods for mathematically modelling the action of photolysis on particular relevant chemical species. We start with a general discussion of mechanisms that transport chemicals within soil §2. There is an existing computational model exploited by Syngenta for such modelling and we discuss how this performs and the predictions that can be derived using it §3. The particular mechanism of photolysis is then considered. One aspect of this mechanism that is investigated is how the roughness of the surface of the soil could be adequately incorporated into the modelling. Some results relating to this are presented §4.2. Some of the original experimental data used to derive aspects of the model of photolysis are revisited and a simple model of the process presented and shown to fit the data very well §5. By considering photolysis with a constant diffusion coefficient various analytical results are derived and general behaviour of the system outlined. This simple model is then applied to real field-based data and shown to give very good fit when simply extended to account for the moisture variations by utilising moisture dependent diffusion coefficients derived from the existing computational model §5.3. Some consequences of the simple model are then discussed §6

Transport Processes in Metal-Insulator Granular Layers

Tunnel transport processes are considered in a square lattice of metallic nanogranules embedded into insulating host to model tunnel conduction in real metal/insulator granular layers. Based on a simple model with three possible charging states ($\pm$, or 0) of a granule and three kinetic processes (creation or recombination of a $\pm$ pair, and charge transfer) between neighbor granules, the mean-field kinetic theory is developed. It describes the interplay between charging energy and temperature and between the applied electric field and the Coulomb fields by the non-compensated charge density. The resulting charge and current distributions are found to be essentially different in the free area (FA), between the metallic contacts, or in the contact areas (CA), beneath those contacts. Thus, the steady state dc transport is only compatible with zero charge density and ohmic resistivity in FA, but charge accumulation and non-ohmic behavior are \emph{necessary} for conduction over CA. The approximate analytic solutions are obtained for characteristic regimes (low or high charge density) of such conduction. The comparison is done with the measurement data on tunnel transport in related experimental systems.Comment: 10 pages, 11 figures, 1 reference corrected, acknowlegments adde

Vibrationally coupled electron transport in single-molecule junctions: The importance of electron-hole pair creation processes

Vibrationally coupled electron transport through single-molecule junctions is considered. Reviewing our recent theoretical work, we show that electron-hole pair creation processes represent the key to understand the vibrational excitation characteristic of a single-molecule contact. Moreover, these processes can lead to a number of interesting transport phenomena such as, for example, negative differential resistance, rectification, mode-selective vibrational excitation and a pronounced temperature dependence of the electrical current. Thus, electron-hole pair creation processes are crucial to elucidate the basic mechanisms of vibrationally coupled electron transport through a single-molecule contact, despite the fact that these processes do not directly contribute to the electrical current that is flowing through the junction.Comment: 13 article pages, 13 figures; review article submitted to PSS (b) for the special issue 'Quantum transport at the molecular scale