Dynamics of a Tagged Particle in the Asymmetric Exclusion Process with the Step Initial Condition

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.     

Large Time Asymptotics of Growth Models on Space-like Paths II: PNG and Parallel TASEP

We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process. The long time scaling limit of the surface height is shown to coincide with the Airy₁ process. This result holds more generally for the observation points located along any space-like path in the space-time plane. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update.     

Asymptotics in ASEP with Step Initial Condition

In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. Here we use this formula to obtain three asymptotic results for the positions of these particles. In one an apparently new distribution function arises and in another the distribution function F ₂ arises. The latter extends a result of Johansson on TASEP to ASEP, and hence proves KPZ universality for ASEP with step initial condition.     

Spontaneous symmetry breaking in asymmetric exclusion process with constrained boundaries and site sharing: A Monte Carlo study

This paper investigates the two species totally asymmetric simple exclusion process (TASEP) with constrained boundaries and site sharing in a one-lane system. The model is reminiscent of pedestrian traffic crossing a narrow pathway in both directions. In boundaries, particles can enter the system only if the corresponding sites are empty. The new aspect of this study compared to previous two species TASEP models is that the oppositely moving particles do not exchange their positions each other but by sharing the same site. Monte Carlo simulations have shown that the spontaneous symmetry breaking is observed in high-low-density phase and asymmetric low-low-density phase. The flipping processes are also observed in both phases. The maximal current phase appears for sufficiently large sharing probability. Histograms of two species of particles and average currents are computed. The results are also compared with the Bridge model [Evans et al., Phys. Rev. Lett. 74 (1995) 208] which means that two species of particles can exchange their positions with a certain probability when they meet together. It is shown that our model exhibits higher current than that in the Bridge model.     

Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process

The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli ρ measure as initial conditions, 0<ρ<1, is stationary in space and time. Let N_t(j) be the number of particles which have crossed the bond from j to j+1 during the time span [0,t]. For we prove that the fluctuations of N_t(j) for large t are of order t^1/3 and we determine the limiting distribution function , which is a generalization of the GUE Tracy-Widom distribution. The family of distribution functions have been obtained before by Baik and Rains in the context of the PNG model with boundary sources, which requires the asymptotics of a Riemann-Hilbert problem. In our work we arrive at through the asymptotics of a Fredholm determinant. is simply related to the scaling function for the space-time covariance of the stationary TASEP, equivalently to the asymptotic transition probability of a single second class particle. An erratum to this article can be found at     

Limit Processes for TASEP with Shocks and Rarefaction Fans

We consider the totally asymmetric simple exclusion process (TASEP) with two-sided Bernoulli initial condition, i.e., with left density ρ ₋ and right density ρ ₊. We study the associated height function, whose discrete gradient is given by the particle occurrences. Macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of ρ _±. We characterize the large time scaling limit of the multipoint fluctuations as a function of the densities ρ _± and of the different macroscopic regions. Moreover, using a slow decorrelation phenomena, the results are extended from fixed time to the whole space-time, except along the some directions (the characteristic solutions of the related Burgers equation) where the problem is still open.     

Determinant Representation for Some Transition Probabilities in the TASEP with Second Class Particles

We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an explicit expression of these quantities in terms of the Bethe wave function. In a next step it is proved rigorously that this expression can be written in a compact determinantal form for the case where the order of the first and second class particles does not change in time. An independent geometrical approach provides insight into these results and enables us to generalize the determinantal solution to the multi-class TASEP.     

Exclusive Queueing Process with Discrete Time

In a recent study (Arita in Phys. Rev. E 80(5):051119, 2009), an extension of the M/M/1 queueing process with the excluded-volume effect as in the totally asymmetric simple exclusion process (TASEP) was introduced. In this paper, we consider its discrete-time version. The update scheme we take is the parallel one. A stationary-state solution is obtained in a slightly arranged matrix product form of the discrete-time open TASEP with the parallel update. We find the phase diagram for the existence of the stationary state. The critical line which separates the parameter space into regions with and without the stationary state can be written in terms of the stationary current of the open TASEP. We calculate the average length of the system and the average number of particles.     

Convergence properties of the cluster expansion for equal- time Green functions in scalar theories

We investigate the convergence properties of the cluster expansion of equal-time Green functions in scalar theories with quartic self-coupling in (0 + 1), (1 + 1), and (2 + 1) space-time dimensions. The computations are carried out within the equal-time correlation dynamics approach, which consists in a closed set of coupled equations of motion for connected Green functions as obtained by a truncation of the BBGKY hierarchy. We find that the cluster expansion shows good convergence as long as the system is in a localized state (single phase configuration) and that it breaks down in a non-localized state (two phase configuration), as one would naively expect. Furthermore, in the case of dynamical calculations with a time dependent Hamiltonian for the evaluation of the effective potential we find two timescales determining the adiabaticity of the propagation; these are the time required for adiabaticity in the single phase region and the time required for tunneling into the non-localized lowest energy state in the two phase region. Our calculations show a good convergence for the effective potentials in (1 + 1) and (2+1) space-time dimensions since tunneling is suppressed in higher space-time dimensions.     

Correlations of neutral and charged particles in 40Ar- 58Ni reaction at 77 MeV/u

The measurement of the two-particle correlation function for different particle species allows to obtain information about the development of the particle emission process: the space-time properties of emitting sources and the emission time sequence of different particles. The single-particle characteristics and two-particle correlation functions for neutral and charged particles registered in forward direction are used to determine that the heavy fragments (deuterons and tritons) are emitted in the first stage of the reaction (pre-equilibrium source) while the majority of neutrons and protons originates from the long-lived quasi-projectile. The emission time sequence of protons, neutrons and deuterons has been obtained from the analysis of non-identical particle correlation functions.     

Fractional backward Kolmogorov equations

This paper derives the fractional backward Kolmogorov equations in fractal space-time based on the construction of a model for dynamic trajectories. It shows that for the type of fractional backward Kolmogorov equation in the fractal time whose coefficient functions are independent of time, its solution is equal to the transfer probability density function of the subordinated process X(Sα(t)), the subordinator Sα(t) is termed as the inverse-time α-stable subordinator and the process X(τ) satisfies the corresponding time homogeneous Ito stochastic differential equation.     

Pion-proton correlations and asymmetry measurement in Au + Au collisions at √<Emphasis Type="Italic">s</Emphasis><Subscript><Emphasis Type="Italic">NN</Emphasis></Subscript> = 200 GeV data

Correlations between non-identical particles at small relative velocity probe asymmetries in the average space-time emission points at freeze-out. The origin of such asymmetries may be from long-lived resonances, bulk collective effects, or differences in the freeze-out scenario for the different particle species. STAR has extracted pion-proton correlation functions from a dataset of Au+Au collisions at √s _NN = 200 GeV. We present correlation functions in the spherical harmonic decomposition representation, for different centralities and for different combinations of pions and (anti-)protons.     

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, for medium- to low-load conditions, for all chosen influx and outflux rates, we only observe the LD and HD phases, and the maximal-current phase disappears. Further, we also measure the dynamics for a single dynein particle which is logarithmically slower than a TASEP particle with a shorter waiting time. Our results also confirm experimental observations of the dwell time distribution: The dwell time distribution for dyneins is exponential in less crowded conditions, whereas a double exponential emerges under overcrowded conditions.     

Simulation studies of shear viscosity time correlation functions in liquid CS2

The Green—Kubo time correlation function for the shear viscosity in liquid CS₂ has been simulated by molecular dynamics at several thermodynamic state points. The breakdown of this function into its kinetic and potential contributions as well as the cross-term between the two has been performed. Intermolecular interactions were obtained from a three-centre atom—atom (12/6) Lennard-Jones potential model. The time correlation functions for the potential part of the shear viscosity contain component two-, three- and four-body terms that were explicitly evaluated to show that they partially cancel each other at short times but at long times, they exhibit approximately exponential decays with magnitude ratios corresponding to nearly perfect cancellation. In this respect, the correlation functions for CS₂ resemble those of liquid argon. In addition, the microscopic stress tensor was separated into the portions arising from the repulsive and attractive branches of the Lennard-Jones model. This split gives rise to positive autocorrelation functions involving the repulsive and the attractive forces plus a negative cross-correlation function between the two that partially cancels the contributions of the autocorrelation functions. It is argued that the breakdown of the potential part of the shear viscosity into its component parts is helpful in elucidating the role of molecular re-orientation in determining the separate short and long time behaviours of this time correlation function for liquids such as CS₂.     

Non-identical particle correlations in STAR

The correlation function of non-identical particles is sensitive to the relative space-time asymmetries in particle emission. Analysing pion-kaon, pion-proton and kaon-proton correlation functions, measured in the Au+Au collisions by the STAR experiment at RHIC, we show that pions, kaons and protons are not emitted at the same average space-time coordinates. The shifts between pion, kaon and proton sources are consistent with the picture of a transverse collective flow. Results of the first measurement of proton-lambda correlations at STAR are in agreement with recent CERN and AGS data.     

Velocity correlation functions for finite one-dimensional systems

Certain systems consisting of a one-dimensional gas of a finite number of point particles interacting with a “hard-core” potential are considered.We use the technique developed by Jepsen to calculate exactly the velocity correlation functions for these systems. We discover that after a slow decay for times of the order of the relaxation time, there is a “fast” decay to the equilibrium value on a macroscopic time scale characterized by L/v_TH (L is the length of the container and v_TH the thermal velocity).The dependence of the velocity correlation functions on the initial position of the specified particle is also considered. In particular, the behaviour approaching the boundary of the container is analyzed. These considerations are generalized to systems of higher spatial dimension.     

Formation of the distribution function of the aerosol-particle radii for the hydrolysis products of uranium hexafluoride in industrial premises

We consider UO₂F₂ and HF aerosol particles that formed in the air of industrial premises at a factory of the nuclear industry. The distribution function g ₁ of the aerosol-particle radii at a given space-time point is analyzed. Some of the lognormal distribution functions that are related to a gas-dispersed environment of the working premise are considered. The deviation of g ₁ from lognormal distribution functions is estimated. The related problems of calculating the average transmission coefficients of atoms of toxic substances (uranium or fluorine) in the human body during inhalation are discussed.     

Rotational diffusion of a tracer colloid particle: I. Short time orientational correlations

We extend the generalized Smoluchowski equation to descrbe the diffusional relaxation of position and orientation in a suspension of interacting spherical colloid particles. Considering a tracer particle which interacts with other particles through spherically symmetric pair potentials and with an external field we obtain a cluster expansion representation of the orientational time correlation functions for the tracer. The one and two body cluster contributions are studied explicitly at short times. Working to first order in volume fraction φ we show that the initial slope of the time correlation functions is described by a modified diffusion coefficient D^r = D^r₀(1 −C^rφ) where C^r is a number determined by hydrodynamic and potential interactions. We evaluate C^r numerically for spheres with slip-stick hydrodynamic boundary conditions and also for permeable spheres.     

Relativistic BBGKY Theory and Collision Integral of Generalized Boltzmann Equation in a Relativistic Magnetized Plasma

Usually, only Coulomb interactions between charged particles which are independent of time are considered in BBGKY theory of a nonrelativistic plasma. In relativistic case, the induced electromagnetic forces between charged particles which are dependent on time obviously should be considered. A Lorentz-covariant generalized n-time Liouville equation for classical plasma is established. A convenient form applicable to the laboratory frame of this equation is also given. The relativistic BBGKY hierarchy is developed in which both Coulomb and electromagnetic forces between particles are included. A method for solving the relativistic pair correlation equation is given in polarization approximation. A new formula for calculating collision integral in terms of discrete particle Green functions is given. A number of generalized Boltzmann equations for relativistic plasmas are derived.