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Register a new userPhase diagram of two-lane driven diffusive systems
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We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail.
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We consider networks made of parallel lanes along which particles hop according to driven diffusive dynamics. The particles also hop transversely from lane to lane, hence indirectly coupling their longitudinal dynamics. We present a general method for constructing the phase diagram of these systems which reveals that in many cases their physics reduce to that of single-lane systems. The reduction to an effective single-lane description legitimizes, for instance, the use of a single TASEP to model the hopping of molecular motors along the many tracks of a single microtubule. Then, we show how, in quasi-2D settings, new phenomena emerge due to the presence of non-zero transverse currents, leading, for instance, to strong `shear localisation along the network.
Driven lattice gases as the ASEP are useful tools for the modeling of various stochastic transport processes carried out by self-driven particles, such as molecular motors or vehicles in road traffic. Often these processes take place in one-dimensional systems offering several tracks to the particles, and in many cases the particles are able to change track with a given rate. In this work we consider the case of strong coupling where the hopping rate along the tracks and the exchange rates are of the same order, and show how a phenomenological approach based on a domain wall theory can describe the dynamics of the system. In particular, the domain walls on the different tracks form pairs, whose dynamics dominate the behavior of the system.
When an extended system is coupled at its opposite boundaries to two reservoirs at different temperatures or chemical potentials, it cannot achieve a global thermal equilibrium and is instead driven to a set of current-carrying nonequilibrium states. Despite the broad relevance of such a scenario to metallic systems, there have been limited investigations of the entanglement structure of the resulting long-time states, in part, due to the fundamental difficulty in solving realistic models for disordered, interacting electrons. We investigate this problem by carefully analyzing two toy models for coherent quantum transport of diffusive fermions: the celebrated three-dimensional, noninteracting Anderson model and a class of random quantum circuits acting on a chain of qubits, which exactly maps to a diffusive, interacting fermion problem. Crucially, the random circuit model can also be tuned to have no interactions between the fermions, similar to the Anderson model. We show that the long-time states of driven noninteracting fermions exhibit volume-law mutual information and entanglement, both for our random circuit model and for the nonequilibrium steady-state of the Anderson model. With interactions, the random circuit model is quantum chaotic and approaches local equilibrium, with only short-range entanglement. These results provide a generic picture for the emergence of local equilibrium in current-driven quantum-chaotic systems, and also provide examples of stable, highly-entangled many-body states out of equilibrium. We discuss experimental techniques to probe these effects in low-temperature mesoscopic wires or ultracold atomic gases.
Different phases in open driven systems are governed by either shocks or rarefaction waves. A presence of an isolated umbilic point in bidirectional systems of interacting particles stabilizes an unusual large scale excitation, an umbilic shock (U-shock). We show that in open systems the U-shock governs a large portion of phase space, and drives a new discontinuous transition between the two rarefaction-controlled phases. This is in contrast with strictly hyperbolic case where such a transition is always continuous. Also, we describe another robust phase which takes place of the phase governed by the U-shock, if the umbilic point is not isolated.
In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide class of microscopic stochastic models where they are satisfied. The description however does not refer in any way to an underlying microscopic dynamics: the only input required are transport coefficients as functions of thermodynamic variables, which are experimentally accessible. The basic postulates are local equilibrium which allows a hydrodynamic description of the evolution, the Einstein relation among the transport coefficients, and a variational principle defining the out of equilibrium free energy. Associated to the variational principle there is a Hamilton-Jacobi equation satisfied by the free energy, very useful for concrete calculations. Correlations over a macroscopic scale are, in our scheme, a generic property of nonequilibrium states. Correlation functions of any order can be calculated from the free energy functional which is generically a non local functional of thermodynamic variables. Special attention is given to the notion of equilibrium state from the standpoint of nonequilibrium.
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