Related papers: Small-scale behaviour in deterministic reaction mo…
The Einstein relation describes the response of a diffusing particle to a small constant external force. It states that, as the force tends to zero, the ratio of the limiting velocity to the force magnitude converges to the diffusivity…
Dynamical features of tagged particles are studied in a one dimensional $A+A \rightarrow kA$ system for $k=0$ and 1, where the particles $A$ have a bias $\epsilon$ $(0 \leq \epsilon \leq 0.5)$ to hop one step in the direction of their…
In this article, we consider $\beta$-ensembles, i.e. collections of particles with random positions on the real line having joint distribution $$\frac{1}{Z_N(\beta)}|\Delta(\lambda)|^\beta e^{- \frac{N\beta}{4}\sum_{i=1}^N\lambda_i^2}d…
This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where $\beta N \to const \in (0, \infty)$, with $N$ the system size and $\beta$ the inverse temperature. In this regime, the convergence to…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…
We study the long-range directed polymer model on $\mathbbm{Z}$ in a random environment, where the underlying random walk lies in the domain of attraction of an $\alpha$-stable process for some $\alpha\in(0,2]$. Similar to the more classic…
Dynamical mean-field approximations are performed to study the phase transition of a pair contact process with diffusion in different spatial dimensions. The level of approximation is extended up to 18-site clusters for the one-dimensional…
We examine the long-time behaviour of A+B \to 0 reaction-diffusion systems with initially separated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constant D_A of particles A and initial…
Eigenstates of Bose particles with repulsive contact interactions in one-dimensional space with periodic boundary conditions can be found with the help of the Bethe ansatz. The type~II excitation spectrum identified by E. H. Lieb,…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
A method is introduced to renormalize the zero-range interaction for use in mean-field and many-body theory, starting from two-body calculations. The density-renormalized delta-function interaction is then applied using mean-field theory to…
When two non-relativistic particles scatter in one dimension, they can become entangled. This entanglement process is constrained by the symmetries of the scattering system and the boundary conditions on the incoming state. Applying these…
We consider a classical system of point particles interacting by means of a short range potential. We prove that, in the low--density (Boltzmann--Grad) limit, the system behaves, for short times, as predicted by the associated Boltzmann…
We present a theoretical study on the response properties to an external electric field of strongly correlated one-dimensional metals. Our investigation is based on the recently developed Bethe-Ansatz local density approximation (BALDA) to…
An autocatalytic reacting system with particles interacting at a finite distance is studied. We investigate the effects of the discrete-particle character of the model on properties like reaction rate, quenching phenomenon and front…
An Antisymmetrized Molecular Dynamics model is used to explore the collision of $^{114}$Cd projectiles with $^{92}$Mo target nuclei at E/A=50 MeV over a broad range in impact parameter. The atomic number (Z), velocity, and emission pattern…
A two species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean field equations for general choice of reaction rates have been solved…
Scale-free surfaces, such as cones, remain unchanged under a simultaneous expansion of all coordinates by the same factor. Probability density of a particle diffusing near such absorbing surface at large time approaches a simple form that…
In discrete contexts such as the degree distribution for a graph, \emph{scale-free} has traditionally been \emph{defined} to be \emph{power-law}. We propose a reasonable interpretation of \emph{scale-free}, namely, invariance under the…
New experimental results for the elastic scattering of 6He on 64Zn at incident energies of 15.0 and 18.0 MeV and 4He at 17.5 MeV along with results already published at 10.0 and 13.6 MeV, are presented. Elastic and alpha experimental cross…