Spectral gaps of open TASEP in the maximal current phase

gTASEP with attraction interaction on lattices with open boundaries

We study a model of aggregation and fragmentation of clusters of particles on an open segment of a single-lane road. The particles and clusters obey the stochastic discrete-time discrete-space kinetics of the Totally Asymmetric Simple Exclusion Process (TASEP) with backward ordered sequential update (dynamics), endowed with two hopping probabilities, p and pm. The second modified probability, pm, models a special kinematic interaction between the particles belonging to the same cluster. This modification is called generalized TASEP (gTASEP) since it contains as special cases TASEP with paralle…

Dynein-inspired multilane exclusion process with open boundary conditions

Motivated by the sidewise motions of dynein motors shown in experiments, we use a variant of the exclusion process to model the multistep dynamics of dyneins on a cylinder with open ends. Due to the varied step sizes of the particles in a quasi-two-dimensional topology, we observe the emergence of a novel phase diagram depending on the various load conditions. Under high-load conditions, our numerical findings yield results similar to the TASEP model with the presence of all three standard TASEP phases, namely the low-density (LD), high-density (HD), and maximal-current (MC) phases. However, f…

Exclusion process on an open lattice with fluctuating boundaries

We show that the TASEP of a driven system of particles of arbitrary size, with nearest neighbor repulsive interaction, on an open lattice is equivalent to the TASEP of interacting monomers on an open lattice whose size fluctuates in response to the entry and exit of particles. We have presented the maximal current profile as a function of the interaction strength for dimers and tetramers, obtained in Monte Carlo simulation; the results agree well with the ones computed by applying a specific rod-to-monomer mapping to the steady state current and density predicted by a mean-field theory of inte…

The asymmetric Exclusion Process and Brownian Excursions

We consider the totally asymmetric exclusion process (TASEP) in one dimension in its maximal current phase. We show, by an exact calculation, that the non-Gaussian part of the fluctuations of density can be described in terms of the statistical properties of a Brownian excursion. Numerical simulations indicate that the description in terms of a Brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase.

Boundary induced phase transition with stochastic entrance and exit

We study an open-chain totally asymmetric exclusion process (TASEP) with stochastic gates present at the two boundaries. The gating dynamics has been modeled keeping the physical system of ion-channel gating in mind. These gates can randomly switch between an open state and a closed state. In the open state, the gates are highly permeable such that any particle arriving at the gate immediately passes through. In the closed state, a particle gets trapped at the gate and cannot pass through until the gate switches open again. We calculate the phase-diagram of the system and find important and no…

Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with particle nonconservation

We study asymmetric exclusion processes (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or {\em defects}. We allow weak particle nonconservation via Langmuir kinetics (LK), that are parameterised by generic unequal attachment and detachment rates. For an extended defect, in the thermodynamic limit the system generically displays inhomogeneous density profiles in the steady state - the faster segment is either in a phase with spatially varying density having no density discontinuity, or a phase with a discontinuous density changes. Nonequili…

Non-equilibrium processes: driven lattice gases, interface dynamics, and quenched disorder effects on density profiles and currents

Properties of the one-dimensional totally asymmetric simple exclusion process (TASEP), and their connection with the dynamical scaling of moving interfaces described by a Kardar-Parisi-Zhang (KPZ) equation are investigated. With periodic boundary conditions, scaling of interface widths (the latter defined via a discrete occupation-number-to-height mapping), gives the exponents $α=0.500(5)$, $z=1.52(3)$, $β=0.33(1)$. With open boundaries, results are as follows: (i) in the maximal-current phase, the exponents are the same as for the periodic case, and in agreement with recent Bethe ansatz resul…

Renyi entropy of the totally asymmetric exclusion process

The Renyi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the Renyi entropy of the totally asymmetric exclusion process (TASEP). We calculate explicitly an entropy whereby the squares of configuration probabilities are summed, using the matrix product formalism to map the problem to one involving a six direction lattice walk in the upper quarter plane. We derive the generating function across the whole phase diagram, using an obstinate kernel method. This gives the leading behaviour of the Renyi entr…

Bottleneck-induced transitions in a minimal model for intracellular transport

We consider the influence of disorder on the non-equilibrium steady state of a minimal model for intracellular transport. In this model particles move unidirectionally according to the \emph{totally asymmetric exclusion process} (TASEP) and are coupled to a bulk reservoir by \emph{Langmuir kinetics}. Our discussion focuses on localized point defects acting as a bottleneck for the particle transport. Combining analytic methods and numerical simulations, we identify a rich phase behavior as a function of the defect strength. Our analytical approach relies on an effective mean-field theory obtain…

恒定电路深度下的一维量子吉布斯态

One-dimensional quantum Gibbs states in constant circuit depth

本文证明任意恒定温度下自旋链的吉布斯态可分解为有界块乘积态混合，从而可用恒定深度局域电路制备，并限制热纠缠结构，同时推广到费米子系统。