Related papers: Born-Oppenheimer Approximation for a Singular Syst…
The principles of behavior of the system with discrete interactions are applied to description of motion of the relativistic particle. Applying the concept of non-local behavior both to position in space and to time, the apparently…
We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state…
The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and…
We give a thorough analysis of the convergence properties of the configuration-interaction method as applied to parabolic quantum dots among other systems, including \emph{a priori} error estimates. The method converges slowly in general,…
We explore the spatial features of various orders of Fraunhofer diffraction patterns in a four-level N-type atomic system. The system interacts with a weak probe light, a standing wave (SW) coupling field in the x-direction, and a…
Under the influence of gravity, light scalar fields can form bound compact objects called boson stars. We use the technique of matching asymptotic expansions to obtain the profile for boson stars where the constituent particles have…
We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a…
We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence for second order systems under suitable contraction…
In most theoretical descriptions of collective strong coupling of organic molecules to a cavity mode, the molecules are modeled as simple two-level systems. This picture fails to describe the rich structure provided by their internal…
Scalar particles are a common prediction of many beyond the Standard Model theories. If they are light and cold enough, there is a possibility they may form Bose-Einstein condensates, which will then become gravitationally bound. These…
The complex method to obtain 2-dimensional Born-Infeld electrostatic solutions is presented in a renewed form. The solutions are generated by a holomorphic seed that makes contact with the Coulombian complex potential. The procedure is…
We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the…
We provide a rigorous derivation of the Boltzmann equation as the mesoscopic limit of systems of hard spheres, or Newtonian particles interacting via a short-range potential, as the number of particles $N$ goes to infinity and the…
We consider the problem of a single particle interacting with $N$ identical fermions, at zero temperature and in one dimension. We calculate the binding energy as well as the effective mass of the single particle. We use an approximate…
The motion of a continuum of matter subject to gravitational interaction is classically described by the Euler-Poisson system. Prescribing the density of matter at initial and final times, we are able to obtain weak solutions for this…
We consider a hamiltonian system on the real line, consisting of real scalar field $\phi(x,t)$ and point particle with trajectory $y(t)$. The dynamics of this system is defined by the system of two equations: wave equation for the field,…
The gravitational-radiation-induced inspiral of a binary system of compact objects is considered. A scheme is described to model the regime in which the gravitational interaction is too strong to use weak-field approximation methods, but…
A simple kinematical argument suggests that the classical approximation may be inadequate to describe the evolution of a system with an anisotropic particle distribution. In order to verify this quantitatively, we study the Boltzmann…
Motivated by a paper by B.T. Sutcliffe and R.G. Woolley, we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for…
Impurities immersed into a surrounding ultra-cold Bose gas experience interactions mediated by the surrounding many-body environment. If one focuses on two impurities that are sufficiently close to each other, they can form a bipolaron…