Related papers: Ground States in the Diffusion-Dominated Regime
We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles…
Using the density matrix formalism, we prove an existence theorem of the periodic steady-state for an arbitrary periodically-driven system. This state has the same period as the modulated external influence, and it is realized as an…
The hydrodynamic stationary states of a granular fluid are addressed theoretically when subject to energy injection and a time-independent, but otherwise arbitrary external potential force. When the latter is not too symmetrical in a well…
Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is…
This article considers the generative modeling of the (mixed) states of quantum systems, and an approach based on denoising diffusion model is proposed. The key contribution is an algorithmic innovation that respects the physical nature of…
The asymmetric simple exclusion process with additional Langmuir kinetics, i.e. attachment and detachment in the bulk, is a paradigmatic model for intracellular transport. Here we study this model in the presence of randomly distributed…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
The dynamics of interacting particles in orbital magnetic fields are notoriously difficult to study, as this physics is inherently connected to electronic correlations in two-dimensional systems, for which no straightforward theoretical…
We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually…
Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state…
We consider the rate of transition for a particle between two metastable states coupled to a thermal environment for various magnitudes of the coupling strength, using the recently proposed infrequent metadynamics approach (Tiwary and…
We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we…
In this paper we deal with further recent developments, strictly connected to the recent result obtained by Basile, Nota, Pezzotti and Pulvirenti. We consider the Lorentz gas out of equilibrium in a weak coupling regime. Each obstacle of…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…
Large transporting regular islands are found in the classical phase space of a modified kicked rotor system in which the kicking potential is reversed after every two kicks. The corresponding quantum system, for a variety of system…
We present an ``orbital'' free density functional theory for computing the quantum ground state of atomic clusters and liquids. Our approach combines the Bohm hydrodynamical description of quantum mechanics with an information theoretical…
In this paper, we analyze the dynamics of an $N$ particles system evolving according the gradient flow of an energy functional. The particle system is a consistent approximation of the Lagrangian formulation of a one parameter family of…
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 diffusion of charged particles in stationary stochastic magnetic field ${\bf B}$ with zero mean, $\langle {\bf B} \rangle = 0 $. In the case when electric current is carried by electrons, the field is force-free, $\mathrm{curl}…