Related papers: Conservation Laws and Integrability of a One-dimen…
We discuss dynamical aspects of an asymmetric version of assisted diffusion of hard core particles on a ring studied by G. I. Menon {\it et al.} in J. Stat Phys. {\bf 86}, 1237 (1997). The asymmetry brings in phenomena like kinematic waves…
One dimensional systems sometimes show pathologically slow decay of currents. This robustness can be traced to the fact that an integrable model is nearby in parameter space. In integrable models some part of the current can be conserved,…
We study the diffusion of classical hard-core particles in disordered lattices within the formalism of a quantum spin representation. This analogy enables an exact treatment of non-instantaneous correlation functions at finite particle…
We consider a simple analytically tractable model of metastability and ageing. In this model, a particle can jump left or right by two steps to an unoccupied site, but only if the the site in between is occupied. We show that the model is…
We show that hydrodynamic diffusion is generically present in many-body interacting integrable models. We extend the recently developed generalised hydrodynamic (GHD) to include terms of Navier-Stokes type which lead to positive entropy…
We describe the crossover from generalized hydrodynamics to conventional hydrodynamics in nearly integrable systems. Integrable systems have infinitely many conserved quantities, which spread ballistically in general. When integrability is…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We study a model of stochastic deposition-evaporation with recombination, of three species of dimers on a line. This model is a generalization of the model recently introduced by Barma {\it et. al.} (1993 {\it Phys. Rev. Lett.} {\bf 70}…
This article is concerned with the dynamics of a mixture of gases. Under the assumption that all the gases are isothermal and inviscid, we show that the governing equations have an elegant conservation-dissipation structure. With the help…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We consider the large-time dynamics of one-dimensional processes involving adsorption and desorption of extended hard-core particles (dimers, trimers,\,$\cdots,k$-mers), while interacting through their constituent monomers. Desorption can…
A driven system of three species of particle diffusing on a ring is studied in detail. The dynamics is local and conserves the three densities. A simple argument suggesting that the model should phase separate and break the translational…
We study analytically a model where particles with a hard-core repulsion diffuse on a finite one-dimensional lattice with space-dependent, asymmetric hopping rates. The system dynamics are given by the \mbox{U$_{q}$[SU(2)]}-symmetric…
We analytically investigate a 1d branching-coalescing model with reflecting boundaries in a canonical ensemble where the total number of particles on the chain is conserved. Exact analytical calculations show that the model has two…
A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the…
We consider spin chain models with local Hamiltonians that display weak ergodicity breaking. In these models, the majority of the eigenstates are thermal, but there is a distinguished subspace of the Hilbert space in which ergodicity is…
Given a first-order nonlinear hyperbolic system of conservation laws endowed with a convex entropy-entropy flux pair, we can consider the class of weak solutions containing shock waves depending upon some small scale parameters. In this…
We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…