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Register a new userDomain wall theory and non-stationarity in driven flow with exclusion
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Added by
Sergio L. A. de Queiroz
Publication date
2016
fields
Physics
and research's language is
English
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We study the dynamical evolution toward steady state of the stochastic non-equilibrium model known as totally asymmetric simple exclusion process, in both uniform and non-uniform (staggered) one-dimensional systems with open boundaries. Domain-wall theory and numerical simulations are used and, where pertinent, their results are compared to existing mean-field predictions and exact solutions where available. For uniform chains we find that the inclusion of fluctuations inherent to the domain-wall formulation plays a crucial role in providing good agreement with simulations, which is severely lacking in the corresponding mean-field predictions. For alternating-bond chains the domain-wall predictions for the features of the phase diagram in the parameter space of injection and ejection rates turn out to be realized only in an incipient and quantitatively approximate way. Nevertheless, significant quantitative agreement can be found between several additional domain-wall theory predictions and numerics.
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The totally asymmetric simple exclusion process (TASEP), a well-known model in its strictly one-dimensional (chain) version, is generalized to cylinder (nanotube) and ribbon (nanoribbon) geometries. A mean-field theoretical description is given for very narrow ribbons (necklaces), and nanotubes. For specific configurations of bond transmissivity rates, and for a variety of boundary conditions, theory predicts equivalent steady state behavior between (sublattices on) these structures and chains. This is verified by numerical simulations, to excellent accuracy, by evaluating steady-state currents. We also numerically treat ribbons of general width. We examine the adequacy of this model to the description of electronic transport in carbon nanotubes and nanoribbons, or specifically-designed quantum dot arrays.
We present a simplified description for spin-dependent electronic transport in honeycomb-lattice structures with spin-orbit interactions, using generalizations of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. Mean field theory and numerical simulations are used to study currents, density profiles and current polarization in quasi- one dimensional systems with open boundaries, and externally-imposed particle injection ($alpha$) and ejection ($beta$) rates. We investigate the influence of allowing for double site occupancy, according to Paulis exclusion principle, on the behavior of the quantities of interest. We find that double occupancy shows strong signatures for specific combinations of rates, namely high $alpha$ and low $beta$, but otherwise its effects are quantitatively suppressed. Comments are made on the possible relevance of the present results to experiments on suitably doped graphenelike structures.
We present a mean-field theory for the dynamics of driven flow with exclusion in graphenelike structures, and numerically check its predictions. We treat first a specific combination of bond transmissivity rates, where mean field predicts, and numerics to a large extent confirms, that the sublattice structure characteristic of honeycomb networks becomes irrelevant. Dynamics, in the various regions of the phase diagram set by open boundary injection and ejection rates, is then in general identical to that of one-dimensional systems, although some discrepancies remain between mean-field theory and numerical results, in similar ways for both geometries. However, at the critical point for which the characteristic exponent is z = 3/2 in one dimension, the mean-field value z = 2 is approached for very large systems with constant (finite) aspect ratio. We also treat a second combination of bond (and boundary) rates where, more typically, sublattice distinction persists. For the two rate combinations, in continuum or late-time limits, respectively, the coupled sets of mean-field dynamical equations become tractable with various techniques and give a two-band spectrum, gapless in the critical phase. While for the second rate combination quantitative discrepancies between mean-field theory and simulations increase for most properties and boundary rates investigated, theory still is qualitatively correct in general, and gives a fairly good quantitative account of features such as the late-time evolution of density profile differences from their steady-state values.
We consider fluctuations of steady-state current activity, and of its dynamic counterpart, the local current, for the one-dimensional totally asymmetric simple exclusion process. The cumulants of the integrated activity behave similarly to those of the local current, except that they do not capture the anomalous scaling behavior in the maximal-current phase and at its boundaries. This indicates that the systemwide sampling at equal times, characteristic of the instantaneous activity, overshadows the subtler effects which come about from non-equal time correlations, and are responsible for anomalous scaling. We show that apparently conflicting results concerning asymmetry (skewness) of the corresponding distributions can in fact be reconciled, and that (apart from a few well-understood exceptional cases) for both activity and local current one has positive skew deep within the low-current phase, and negative skew everywhere else.
We present a numerical study of a two-lane version of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally-imposed particle injection ($alpha$) and ejection ($beta$) rates, spontaneous symmetry breaking can occur. We investigate the statistics and internal structure of the stochastically-induced transitions, or flips, which occur between opposite broken-symmetry states as the system evolves in time. From the distribution of time intervals separating successive flips, we show that the evolution of the associated characteristic times against externally-imposed rates yields information regarding the proximity to a critical point in parameter space. On short time scales, we probe for the possible existence of precursor events to a flip between opposite broken-symmetry states. We study an adaptation of domain-wall theory to mimic the density reversal process associated with a flip.
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