We present a detailed derivation of the renormalization group equations for two dimensional electromagnetic Coulomb gases whose charges lie on a triangular lattice (magnetic charges) and its dual (electric charges). The interactions between the charges involve both angular couplings and a new electromagnetic potential. This motivates the denomination of “elastic” Coulomb gas. Such elastic Coulo...

We report the observation of change in one-dimensional Coulomb interaction between electrons in multi-walled carbon nanotubes (MWNTs). The results indicate occurrence of the phase transition from the Tomonaga-Luttinger liquid (TLL) states within repulsive Coulomb interaction to the superconductive (SC) phase within attractive Coulomb interaction mediated by phonon, as energy decreases. The smal...

We study Coulomb interacting electrons confined in polygonal quantum rings. We focus on the interplay of localization at the polygon corners and Coulomb repulsion. Remarkably, the Coulomb repulsion allows the formation of in-gap states, i.e., corner-localized states of electron pairs or clusters shifted to energies that were forbidden for non-interacting electrons, but below the energies of cor...

Coulomb interaction is one of the major time-consuming components in a density functional theory (DFT) calculation. In the last decade, dramatic progresses have been made to improve the efficiency of Coulomb calculation, including continuous fast multipole method (CFMM) and J-engine method, all developed first inside Q-Chem. The most recent development is the advent of Fourier transform Coulomb...

We review the confinement scenario in Coulomb gauge. We show that when thin center vortex configurations are gauge transformed to Coulomb gauge, they lie on the common boundary of the fundamental modular region and the Gribov region. This unifies elements of the Gribov confinement scenario in Coulomb gauge and the center-vortex confinement scenario. We report on recent numerical studies which s...

Using the Keldysh nonequilibrium technique, we study current and the tunnelling magnetoresistance (TMR) in a quantum dot coupled to two ferromagnetic leads (FM-dot-FM). The current is calculated for both parallel and antiparallel lead alignments. Coulomb interaction and spin-flip scattering are taken into account within the quantum dot. Interestingly, we find that these interactions play a cont...

Wellbore stability analysis based on a new true-triaxial failure criterion i Abstract A main aspect of wellbore stability analysis is the selection of an appropriate rock failure criterion. The most commonly used criterion for brittle failure of rocks is the Mohr-Coulomb criterion. This criterion involves only the maximum and minimum principal stresses, σ 1 and σ 3 , and therefore assumes that ...

The forward direction singularity of the non-relativistic Coulomb S-matrix is examined and discussed. The relativistic Coulomb S-matrix to order e is shown to have a similar singularity.

In this paper the fixed-energy amplitude (Green's function) of the relativistic Coulomb system is solved by Duru-Kleinert (DK) method. In the course of the calculations we observe an equivalence between the relativistic Coulomb system and a radial oscillator.