553 research outputs found
Spectral gap of the totally asymmetric exclusion process at arbitrary filling
We calculate the spectral gap of the Markov matrix of the totally asymmetric
simple exclusion process (TASEP) on a ring of L sites with N particles. Our
derivation is simple and self-contained and extends a previous calculation that
was valid only for half-filling. We use a special property of the Bethe
equations for TASEP to reformulate them as a one-body problem. Our method is
closely related to the one used to derive exact large deviation functions of
the TASEP
Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
We derive, using the algebraic Bethe Ansatz, a generalized Matrix Product
Ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional
periodic lattice. In this Matrix Product Ansatz, the components of the
eigenvectors of the ASEP Markov matrix can be expressed as traces of products
of non-commuting operators. We derive the relations between the operators
involved and show that they generate a quadratic algebra. Our construction
provides explicit finite dimensional representations for the generators of this
algebra.Comment: 16 page
Hidden symmetries in the asymmetric exclusion process
We present a spectral study of the evolution matrix of the totally asymmetric
exclusion process on a ring at half filling. The natural symmetries
(translation, charge conjugation combined with reflection) predict only two
fold degeneracies. However, we have found that degeneracies of higher order
also exist and, as the system size increases, higher and higher orders appear.
These degeneracies become generic in the limit of very large systems. This
behaviour can be explained by the Bethe Ansatz and suggests the presence of
hidden symmetries in the model.
Keywords: ASEP, Markov matrix, symmetries, spectral degeneracies, Bethe
Ansatz.Comment: 16 page
Power Spectra of a Constrained Totally Asymmetric Simple Exclusion Process
To synthesize proteins in a cell, an mRNA has to work with a finite pool of
ribosomes. When this constraint is included in the modeling by a totally
asymmetric simple exclusion process (TASEP), non-trivial consequences emerge.
Here, we consider its effects on the power spectrum of the total occupancy,
through Monte Carlo simulations and analytical methods. New features, such as
dramatic suppressions at low frequencies, are discovered. We formulate a theory
based on a linearized Langevin equation with discrete space and time. The good
agreement between its predictions and simulation results provides some insight
into the effects of finite resoures on a TASEP.Comment: 4 pages, 2 figures v2: formatting change
The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm
in non-equilibrium statistical mechanics. We review exact results for the ASEP
obtained by Bethe ansatz and put emphasis on the algebraic properties of this
model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP
are derived from the algebraic Bethe ansatz. Using these equations we explain
how to calculate the spectral gap of the model and how global spectral
properties such as the existence of multiplets can be predicted. An extension
of the Bethe ansatz leads to an analytic expression for the large deviation
function of the current in the ASEP that satisfies the Gallavotti-Cohen
relation. Finally, we describe some variants of the ASEP that are also solvable
by Bethe ansatz.
Keywords: ASEP, integrable models, Bethe ansatz, large deviations.Comment: 24 pages, 5 figures, published in the "special issue on recent
advances in low-dimensional quantum field theories", P. Dorey, G. Dunne and
J. Feinberg editor
A computer-assisted motivational social network intervention to reduce alcohol, drug and HIV risk behaviors among Housing First residents.
BackgroundIndividuals transitioning from homelessness to housing face challenges to reducing alcohol, drug and HIV risk behaviors. To aid in this transition, this study developed and will test a computer-assisted intervention that delivers personalized social network feedback by an intervention facilitator trained in motivational interviewing (MI). The intervention goal is to enhance motivation to reduce high risk alcohol and other drug (AOD) use and reduce HIV risk behaviors.Methods/designIn this Stage 1b pilot trial, 60 individuals that are transitioning from homelessness to housing will be randomly assigned to the intervention or control condition. The intervention condition consists of four biweekly social network sessions conducted using MI. AOD use and HIV risk behaviors will be monitored prior to and immediately following the intervention and compared to control participants' behaviors to explore whether the intervention was associated with any systematic changes in AOD use or HIV risk behaviors.DiscussionSocial network health interventions are an innovative approach for reducing future AOD use and HIV risk problems, but little is known about their feasibility, acceptability, and efficacy. The current study develops and pilot-tests a computer-assisted intervention that incorporates social network visualizations and MI techniques to reduce high risk AOD use and HIV behaviors among the formerly homeless. CLINICALTRIALS.Gov identifierNCT02140359
Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources
We revisit a totally asymmetric simple exclusion process (TASEP) with open
boundaries and a global constraint on the total number of particles [Adams, et.
al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles
into the lattice depends on the number available in the reservoir. Thus, the
total occupation on the lattice feeds back into its filling process. Although a
simple domain wall theory provided reasonably good predictions for Monte Carlo
simulation results for certain quantities, it did not account for the
fluctuations of this feedback. We generalize the previous study and find
dramatically improved predictions for, e.g., the density profile on the lattice
and provide a better understanding of the phenomenon of "shock localization."Comment: 11 pages, 3 figures, v2: Minor change
Time-Dependent Density Functional Theory for Driven Lattice Gas Systems with Interactions
We present a new method to describe the kinetics of driven lattice gases with
particle-particle interactions beyond hard-core exclusions. The method is based
on the time-dependent density functional theory for lattice systems and allows
one to set up closed evolution equations for mean site occupation numbers in a
systematic manner. Application of the method to a totally asymmetric site
exclusion process with nearest-neighbor interactions yields predictions for the
current-density relation in the bulk, the phase diagram of non-equilibrium
steady states and the time evolution of density profiles that are in good
agreement with results from kinetic Monte Carlo simulations.Comment: 11 pages, 3 figure
Asymmetric exclusion model with several kinds of impurities
We formulate a new integrable asymmetric exclusion process with
kinds of impurities and with hierarchically ordered dynamics.
The model we proposed displays the full spectrum of the simple asymmetric
exclusion model plus new levels. The first excited state belongs to these new
levels and displays unusual scaling exponents. We conjecture that, while the
simple asymmetric exclusion process without impurities belongs to the KPZ
universality class with dynamical exponent 3/2, our model has a scaling
exponent . In order to check the conjecture, we solve numerically the
Bethe equation with N=3 and N=4 for the totally asymmetric diffusion and found
the dynamical exponents 7/2 and 9/2 in these cases.Comment: to appear in JSTA
Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
We analyze the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process on a finite
lattice and with the most general open boundary conditions. We extend results
obtained recently for totally asymmetric diffusion [J. de Gier and F.H.L.
Essler, J. Stat. Mech. P12011 (2006)] to the case of partial symmetry. We
determine the finite-size scaling of the spectral gap, which characterizes the
approach to stationarity at large times, in the low and high density regimes
and on the coexistence line. We observe boundary induced crossovers and discuss
possible interpretations of our results in terms of effective domain wall
theories.Comment: 30 pages, 9 figures, typeset for pdflatex; revised versio
- …