Related papers: On a two-particle bound system on the half-line
We show that the introduction of two worldline parameters defines a different approach to computations in the effective field theory approach to the two-body problem in General Relativity and present some preliminary evidence for a…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
The problem of the description of two interacting particles is considered. It is shown that it can be reduced to the description of one particle in an external static potential even in a relativistic case. The method is based on the…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
A two-electron one-dimensional model of a heteroatomic molecule composed of two open-shell atoms is considered. Including only two electrons isolates and examines the effect that the highest occupied molecular orbital has on the Kohn-Sham…
We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they…
In this dissertation a simple Hamiltonian for a system of inter-acting molecules and radiation field is developed from a model of N Two-Level Molecules interacting, via a dipole approximation, with a single mode, quantized radiation field.…
Two-component Bose-Einstein condensates in the miscible phase can support polarization solitary waves, known as magnetic solitons. By calculating the interaction potential between two magnetic solitons, we elucidate the mechanisms and…
The kinematical formalism for describing spinning particles developped by the author is based upon the idea that an elementary particle is a physical system with no excited states. It can be annihilated by the interaction with its…
This paper constructs a new interacting particle system on a two--dimensional lattice with geometric jumps near a boundary which partially reflects the particles. The projection to each horizontal level is Markov, and on every level the…
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…
This paper deals with the theory of collisions between two ultracold particles with a special focus on molecules. It describes the general features of the scattering theory of two particles with internal structure, using a time-independent…
We predict hyper-entanglement generation during binary scattering of mesoscopic bound states, solitary waves in Bose-Einstein condensates containing thousands of identical Bosons. The underlying many-body Hamiltonian must not be integrable,…
We consider a continuous one dimensional model of two charged interacting particles in a random potential. The electric repulsion is strictly one dimensional and it inhibits Anderson localization. In fact, the spectrum is continuous. The…
We examine the behavior of $n$ Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient…
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
We construct a two-class asymmetric interacting particle system with $U_q(so_6)$ or $U_q(so_8)$ symmetry, in which up to two particles may occupy a site if the two particles have different class. The particles exhibit a drift, but there is…
The scattering and bound states of the many-body systems, related to the short-range Dyson model, are studied. First, we show that the scattering states can be realized as coherent states and the scattering Hamiltonian can be connected to a…
We study the Hamiltonian dynamics of a charged particle submitted to a pure magnetic field in a two-dimensional domain. We provide conditions on the magnetic field in a neighbourhood of the boundary to ensure the confinement of the…