The two dimensional two Coulomb centers problem at small intercentre separation

Split dimensional regularization for the Coulomb gauge at two loops

We evaluate the coefficients of the leading poles of the complete two-loop quark self-energy Σ(p) in the Coulomb gauge. Working in the framework of split dimensional regularization, with complex regulating parameters σ and n/2−σ for the energy and space components of the loop momentum, respectively, we find that split dimensional regularization leads to well-defined two-loop integrals, and that...

Two - Dimensional Supersymmetric Quantum Mechanics : Two Fixed Centers of Force ?

The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker–Hill equations in the first approach. When the two centers have the same ...

The screening phase transitions in the two-dimensional Coulomb gas

The Mayer series of a Coulomb gas with fixed ultraviolet cutoff is studied in two dimensions. In particular, we show the existence of infinitely many thresholds T n = (e2/8~k)(11/2n) 1, k =Boltzmann's constant, e=electr ic charge, n = 1, 2,..., which are conjectured to reflect a sequence of transitions from pure multipole phase (the Kosterlitz Thouless region) to a plasma phase (the Debye scree...

Phase diagram of the two-dimensional lattice Coulomb gas

The nature of phase transitions in the two-dimensional ~2D! neutral Coulomb gas ~CG! has remained a topic of considerable interest. The CG can be related via duality transformation to the 2D XY model, and thus to superfluid and superconducting films. The pioneering work of Kosterlitz and Thouless ~KT! showed that, at low charge density, there is a second order transition from an insulating to a...

On the classical two-dimensional one-component Coulomb plasma