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Complete and physically adequate analytical and semi-analytical solutions have been obtained using a practical dimensionless form of kinetic equation assuming azimuthal symmetry and Maxwellian distributions of target plasma species.…
This study presents a solution to the Yakubovsky equations for four-body bound states in momentum space, bypassing the common use of two-body $t-$matrices. Typically, such solutions are dependent on the fully-off-shell two-body…
Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^{\alpha}$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact…
The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are…
We derive, in 2+1 dimensions, classical solutions for metric and motion of two or more spinning particles, in the conformal Coulomb gauge introduced previously. The solutions are exact in the $N$-body static case, and are perturbative in…
Using techniques of effective field theory, we consider the thermodynamical properties of a dilute two-dimensional plasma interacting via a $1/r$ potential. The first one-loop correction to the partition function is already logarithmically…
We consider a set of electrostatic problems relevant for determining the real-space structure and the ground-state energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are…
A Hamiltonian formulation for the classical problem of electromagnetic interaction of two charged relativistic particles is found.
These lectures contain a theoretical introduction to the few-body problem with short-range resonant binary interactions. In the first part we discuss the effective range expansion for the two-body scattering amplitude emphasizing the role…
The problem of 1-dimensional ultra-relativistic scattering of 2 identical charged particles in classical electrodynamics with retarded and advanced interactions is investigated.
The limit relations for the partial derivatives of the two-electron atomic wave functions at the two-particle coalescence lines have been obtained numerically using accurate CFHHM wave functions. The asymptotic solutions of the proper…
Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a time-dependent many-body theory that is based on the two-particle reduced density…
We present results for many-body perturbation theory for the one-body Green's function at finite temperatures using the Matsubara formalism. Our method relies on the accurate representation of the single-particle states in standard Gaussian…
We provide a two dimensional deformation model to describe how soft squishy circular particles respond to external forces and collisions. This model involves formulating mathematical equations and algorithms for the shape of a deformed…
The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the…
We study the many-body problem of charged particles interacting with their self-generated electromagnetic field. We model the dynamics of the particles by the many-body Maxwell-Schr\"odinger system, where the particles are treated quantum…
Representing a strongly interacting multi-particle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave…
We work towards the general solution of the two-body problem in 2+1-dimensional general relativity with a negative cosmological constant. The BTZ solutions corresponding to black holes, point particles and overspinning particles can be…
A time dependent variational principle is used to dequantize a second order quadrupole boson Hamiltonian. The classical equations for the generalized coordinate and the constraint for angular momentum are quantized and then analytically…
The resolution of the Schr\"odinger equation for the translation-invariant $N$-body harmonic oscillator Hamiltonian in $D$ dimensions with one-body and two-body interactions is performed by diagonalizing a matrix $\mathbb{J}$ of order…