Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSpontaneous Jamming in One-Dimensional Systems
121
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the phenomenon of jamming in driven diffusive systems. We introduce a simple microscopic model in which jamming of a conserved driven species is mediated by the presence of a non-conserved quantity, causing an effective long range interaction of the driven species. We study the model analytically and numerically, providing strong evidence that jamming occurs; however, this proceeds via a strict phase transition (with spontaneous symmetry breaking) only in a prescribed limit. Outside this limit, the nearby transition (characterised by an essential singularity) induces sharp crossovers and transient coarsening phenomena. We discuss the relevance of the model to two physical situations: the clustering of buses, and the clogging of a suspension forced along a pipe.
rate research
Read More
We revisit the slow-bond (SB) problem of the one-dimensional (1D) totally asymmetric simple exclusion process (TASEP) with modified hopping rates. In the original SB problem, it turns out that a local defect is always relevant to the system as jamming, so that phase separation occurs in the 1D TASEP. However, crossover scaling behaviors are also observed as finite-size effects. In order to check if the SB can be irrelevant to the system with particle interaction, we employ the condensation concept in the zero-range process. The hopping rate in the modified TASEP depends on the interaction parameter and the distance up to the nearest particle in the moving direction, besides the SB factor. In particular, we focus on the interplay of jamming and condensation in the current-density relation of 1D driven flow. Based on mean-field calculations, we present the fundamental diagram and the phase diagram of the modified SB problem, which are numerically checked. Finally, we discuss how the condensation of holes suppresses the jamming of particles and vice versa, where the partially-condensed phase is the most interesting, compared to that in the original SB problem.
We present a driven diffusive model which we call the Bus Route Model. The model is defined on a one-dimensional lattice, with each lattice site having two binary variables, one of which is conserved (``buses) and one of which is non-conserved (``passengers). The buses are driven in a preferred direction and are slowed down by the presence of passengers who arrive with rate lambda. We study the model by simulation, heuristic argument and a mean-field theory. All these approaches provide strong evidence of a transition between an inhomogeneous ``jammed phase (where the buses bunch together) and a homogeneous phase as the bus density is increased. However, we argue that a strict phase transition is present only in the limit lambda -> 0. For small lambda, we argue that the transition is replaced by an abrupt crossover which is exponentially sharp in 1/lambda. We also study the coarsening of gaps between buses in the jammed regime. An alternative interpretation of the model is given in which the spaces between ``buses and the buses themselves are interchanged. This describes a system of particles whose mobility decreases the longer they have been stationary and could provide a model for, say, the flow of a gelling or sticky material along a pipe.
We study quench dynamics and equilibration in one-dimensional quantum hydrodynamics, which provides effective descriptions of the density and velocity fields in gapless quantum gases. We show that the information content of the large time steady state is inherently connected to the presence of ballistically moving localised excitations. When such excitations are present, the system retains memory of initial correlations up to infinite times, thus evading decoherence. We demonstrate this connection in the context of the Luttinger model, the simplest quantum hydrodynamic model, and in the quantum KdV equation. In the standard Luttinger model, memory of all initial correlations is preserved throughout the time evolution up to infinitely large times, as a result of the purely ballistic dynamics. However nonlinear dispersion or interactions, when separately present, lead to spreading and delocalisation that suppress the above effect by eliminating the memory of non-Gaussian correlations. We show that, for any initial state that satisfies sufficient clustering of correlations, the steady state is Gaussian in terms of the bosonised or fermionised fields in the dispersive or interacting case respectively. On the other hand, when dispersion and interaction are simultaneously present, a semiclassical approximation suggests that localisation is restored as the two effects compensate each other and solitary waves are formed. Solitary waves, or simply solitons, are experimentally observed in quantum gases and theoretically predicted based on semiclassical approaches, but the question of their stability at the quantum level remains to a large extent an open problem. We give a general overview on the subject and discuss the relevance of our findings to general out of equilibrium problems.
We study approach to the large-time jammed state of the deposited particles in the model of random sequential adsorption. The convergence laws are usually derived from the argument of Pomeau which includes the assumption of the dominance, at large enough times, of small landing regions into each of which only a single particle can be deposited without overlapping earlier deposited particles and which, after a certain time are no longer created by depositions in larger gaps. The second assumption has been that the size distribution of gaps open for particle-center landing in this large-time small-gaps regime is finite in the limit of zero gap size. We report numerical Monte Carlo studies of a recently introduced model of random sequential adsorption on patterned one-dimensional substrates that suggest that the second assumption must be generalized. We argue that a region exists in the parameter space of the studied model in which the gap-size distribution in the Pomeau large-time regime actually linearly vanishes at zero gap sizes. In another region, the distribution develops a threshold property, i.e., there are no small gaps below a certain gap size. We discuss the implications of these findings for new asymptotic power-law and exponential-modified-by-a-power-law convergences to jamming in irreversible one-dimensional deposition.
We study the approach to equilibrium of the event-chain Monte Carlo (ECMC) algorithm for the one-dimensional hard-sphere model. Using the connection to the coupon-collector problem, we prove that a specific version of this local irreversible Markov chain realizes perfect sampling in O(N^2 log N) events, whereas the reversible local Metropolis algorithm requires O(N^3 log N) time steps for mixing. This confirms a special case of an earlier conjecture about O(N^2 log N) scaling of mixing times of ECMC and of the forward Metropolis algorithm, its discretized variant. We furthermore prove that sequential ECMC (with swaps) realizes perfect sampling in O(N^2) events. Numerical simulations indicate a cross-over towards O(N^2 log N) mixing for the sequential forward swap Metropolis algorithm, that we introduce here. We point out open mathematical questions and possible applications of our findings to higher-dimensional statistical-physics models.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
