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Using an analytically tractable lattice model for reaction-diffusion processes of hard-core particles we demonstrate that under nonequilibrium conditions phase coexistence may arise even if the system is effectively one-dimensional as e.g.…
Diffusive properties of a monodisperse system of interacting particles confined to a \textit{quasi}-one-dimensional (Q1D) channel are studied using molecular dynamics (MD) simulations. We calculate numerically the mean-squared displacement…
Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs).…
There has been much interest in semiconductor superlattices because of showing very low thermal conductivities. This makes them especially suitable for applications in a variety of devices for thermoelectric generation of energy, heat…
We have shown that the partition function of the Asymmetric Simple Exclusion Process with open boundaries in a sublattice-parallel updating scheme is equal to that of a two-dimensional one-transit walk model defined on a diagonally rotated…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
The structural properties of confined single-file hard-disk fluids are studied analytically by means of a mapping of the original system onto a one-dimensional mixture of non-additive hard rods, the mapping being exact in the polydisperse…
We solve a non-equilibrium statistical mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size \Delta diffusing in a one dimensional system of finite…
We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of…
In this paper we intend to present a unified treatment of a variety of singular interacting particle systems and their McKean-Vlasov limits. This unified approach is based on the use of the relative entropy on the path space in the spirit…
Single file diffusion (SFD) exhibits anomalously slow collective transport when particles are able to immobilize by binding and unbinding to the one-dimensional channel within which the particles diffuse. We have explored this system for…
A one dimensional exclusion process is introduced where particles hop to a neighbouring vacant site with a rate that depends on the size of the block they belong to. This model is equivalent to a zero range process (ZRP) and shares the same…
For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions,…
We consider a gas of point particles moving on the one-dimensional line with a hard-core inter-particle interaction that prevents particle crossings --- this is usually referred to as single-file motion. The individual particle dynamics can…
The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as…
We study a model of assisted diffusion of hard-core particles on a line. The model shows strongly ergodicity breaking : configuration space breaks up into an exponentially large number of disconnected sectors. We determine this…
We consider the single-file dynamics of $N$ identical random walkers moving with diffusivity $D$ in one dimension (walkers bounce off each other when attempting to overtake). Additionally, we require that the separation between neighboring…
The close similarity between the hierarchies of multiple-point correlation functions for the diffusion-limited coalescence and annihilation processes has caused some recent confusion, raising doubts as to whether such hierarchies uniquely…
We evaluate the self-diffusion and transport diffusion of interacting particles in a discrete geometry consisting of a linear chain of cavities, with interactions within a cavity described by a free-energy function. Exact analytical…
Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong…