Related papers: Higher Dimensional Coulomb Gases and Renormalized …
Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…
The Hubbard model extended by either nearest-neighbour Coulomb correlation and/or nearest neighbour Heisenberg exchange is solved analytically for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the…
The liquid-gas phase transition is analyzed from the topologic properties of the event distribution in the obervables space. A multi-canonical formalism allows to directly relate the standard phase transition with neutral particles to the…
The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetric in the way the boundary conditions at $r=0$ and $r \rightarrow \infty$ are…
We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field limiting regime, the dynamics is described by the Hartree-Fock equation. This extends previous work of Bardos et al. to the case of…
The interplay and competition of magnetic and superconducting correlations in the weakly interacting two-dimensional Hubbard Model is investigated by means of the functional renormalization group. At zero temperature the flow of…
The interaction of electrically charged particles in a dilute gas of point--like magnetic dipoles is studied. We show that the interaction potential at small distances has a linear piece due to overlap of the dipole clouds gathered near…
By solving the exact master equation of open quantum systems, we formulate the quantum thermodynamics from weak to strong couplings. The open quantum systems exchange matters, energies and information with their reservoirs through quantum…
We derive the leading order asymptotics of the logarithmic potential of a two dimensional Coulomb gas at arbitrary positive temperature. The proof is based on precise evaluation of exponential moments, and the theory of Gaussian…
We present a unified framework for studying Coulomb interactions in arbitrary environments using macroscopic quantum electrodynamics on the basis of the electromagnetic Green's function. Our theory can be used to derive the Coulomb…
A simple exactly solvable model is proposed for describing the decays $\Upsilon (4S) \rightarrow B^0\bar B^0$ and $\Upsilon (4S) \rightarrow B^+B^-$. Our predictions agree with available experimental data. Using this model, we analyze the…
Using the renormalization method introduced in \cite{GJ}, we prove what we call the {\em local} Boltzmann-Gibbs principle for conservative, stationary interacting particle systems in dimension $d=1$. As applications of this result, we…
A tight binding model of electrons interacting via bare Coulomb repulsion is numerically investigated by use of the Density Matrix Renormalization Group method which we prove applicable also to very long range potentials. From the analysis…
We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling approximation, and show that they are important at small values of the angular…
We obtain for the attractive Dirac delta-function potential in two-dimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional transmutation is carried out before…
In this paper, we investigate new integrable extensions of two-center Coulomb systems. We study the most general $n$-dimensional deformation of the two-center problem by adding arbitrary functions supporting second order commuting conserved…
The Coulomb gas partition sum is rewritten in terms of the path integrals formalism. It is shown that perturbation theories based on the Mayer expansion and on the path integrals method lead to the identical results. The well known…
We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional…
The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed:…
We present analytic formulas for the ground state energy of the two-dimensional (2D) anyon gas in the quantum limit of a perpendicular magnetic field (Landau level filling factor \nu_L\le 1). These formulas, for the cases without and with…