Related papers: Tagged particle process in continuum with singular…
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…
Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…
We develop an approximate second quantization method for describing the many-particle systems in the presence of bound states of particles at low energies (the kinetic energy of particles is small in comparison to the binding energy of…
Systems of particles interacting via inverse-power law potentials have an invariance with respect to changes in length and temperature, implying a correspondence in the dynamics and thermodynamics between different `isomorphic' sets of…
In this short note we show that any action for $N$ interacting particles can be made invariant under gauged Galilean transformations. While resulting Lagrangian is generally very complicated its Hamiltonian has simple form with first class…
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…
In this paper, we prove the existence of infinite Gibbs Delaunay Potts tessellations for marked particle configurations. The particle systems has two types of interaction, a so-called \emph{background potential} ensures that small and large…
We study a driven system in which interaction between particles causes their directional, coupled movement. In that model system, two particles move alternatingly in time on two coupled chains. Without interaction, both particles diffuse…
We study a system of stochastic differential equations with singular drift which describes the dynamics of signed particles in two dimensions interacting by the Coulomb potential. In contrast to the well-studied cases of identical particles…
Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…
Using the approach to quantum entanglement based on the quantum fluctuations of observables, we show the existence of perfect entangled states of a single "spin-1" particle. We give physical examples related to the photons, condensed matter…
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…
A unified and fully relativistic treatment of the interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is given. New forces on the particle due to the combined effect of electric and magnetic…
Entropy production of an active particle in an external potential is identified through a thermodynamically consistent minimal lattice model that includes the chemical reaction providing the propulsion and ordinary translational noise. In…
We study dissipative dynamics constructed by means of non-commutative Dirichlet forms for various lattice systems with multiparticle interactions associated to CCR algebras. We give a number of explicit examples of such models. Using an…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
For the two-sided Bernoulli initial condition with density $\rho_-$ (resp. $\rho_+$) to the left (resp. to the right), we study the distribution of a tagged particle in the one dimensional symmetric simple exclusion process. We obtain a…
We investigate dynamics of deformable self-propelled particles with a repulsive interaction whose magnitude depends on the relative direction of elongation of a pair of particles. A collective motion of the particles appears in two…
We consider a field theory describing interacting nonrelativistic particles of two types, which map to each other under time reversal, with point-like interaction. We identify a new type of interaction which depends on the relative velocity…
The electrostatic force on a spherical particle near a planar surface is calculated for the cases of a uniform electric field applied in either normal or tangential direction to the surface. The particle and suspending media are assumed to…