Related papers: Equivalence of a one-dimensional driven-diffusive …
We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating…
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…
We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to another particle if the particle carrying this state…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
It was recently suggested by Blythe and Evans that a properly defined steady state normalisation factor can be seen as a partition function of a fictitious statistical ensemble in which the transition rates of the stochastic process play…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of $N$ particles is studied and it is described by use of the…
We characterize a close connection between the continuous-time quantum-walk model and a discrete-time quantum-walk version, based on the staggered model with Hamiltonians in a class of Cayley graphs, which can be considered as a…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
We investigate path-wise observables in experiments on driven colloids in a periodic light field to dissect selected intricate transport features, kinetics, and transition-path time statistics out of thermodynamic equilibrium. These…
The thermal ratchets model toggles a spatially periodic asymmetric potential to rectify random walks and achieve transport of diffusing particles. We numerically solve the governing equation for the full dynamics of an infinite 1D ratchet…
We present an investigation of many-particle quantum walks in systems of non-interacting distinguishable particles. Along with a redistribution of the many-particle density profile we show that the collective evolution of the many-particle…
Dynamic evolution behaviors of dimension-varying control systems often appear in the genetic regulatory network and the vehicle clutch system etc. An interesting and significant study on dimension-varying control systems is how to realize…
A class of models of driven diffusive systems which is shown to exhibit phase separation in $d=1$ dimensions is introduced. Unlike all previously studied models exhibiting similar phenomena, here the phase separated state is fluctuating in…
Driven diffusive systems have provided simple models for non-equilibrium systems with non-trivial structures. Steady state behaviour of these systems with constant boundary conditions have been studied extensively. Comparatively less work…
We follow up an earlier work (briefly reviewed below) to investigate the temporal stability of an exact travelling front solution, constructed in the form of an integral expression, for a one-dimensional discrete Nagumo-like model without…
We introduce a discrete-time quantum dynamics on a two-dimensional lattice that describes the evolution of a $1+1$-dimensional spin system. The underlying quantum map is constructed such that the reduced state at each time step is…
We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems, based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null…
We study a system of diffusing-aggregating particles with deposition and evaporation of monomers. By combining theoretical and numerical methods, we establish a clearer understanding of the non-equilibrium phase transition known to occur in…
A system that violates detailed balance evolves asymptotically into a nonequilibrium steady state with non-vanishing currents. Analogously, when detailed balance holds at any instant of time but the system is driven through time-periodic…