We present a fast and accurate algorithm for the evaluation of nonlocal (longrange) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the convolution of an interaction kernel U(x) and a density function ρ(x) = |ψ(x)|2 for some complexvalued wave function ψ(x), permitting the formal use of Fourier methods. These are hampered by the fact that the Fourier tran...

as we show below in (30). Indeed, the conditions on the coefficients aα are relaxed to be ‘symbolic’, so that for instance a0(z) = φ(z)|z|−ρ, φ ≡ 0 near the origin, ≡ 1 near infinity is allowed. Thus, in particular operators such as ∆+V , where V is the Coulomb potential, without its singularity at the origin, fit into this framework. More generally, we can consider Riemannian metrics g with gi...

For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and V (x) = g/x with the coefficient g in a certain range (x being a space coordinate in one or more dimensions), the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physica...

Electron doping turns semiconductors conductive even when they have wide fundamental band gaps. The degenerate electron gas in the lowest conduction-band states, e.g., of a transparent conducting oxide, drastically modifies the Coulomb interaction between the electrons and, hence, the optical properties close to the absorption edge. We describe these effects by developing an ab initio technique...

We perform a numerical study using both determinantal and constrain path Monte Carlo methods to investigate the magnetic and pairing properties of the single-band Hubbard model on the triangular lattice. We find that the system in the filling region n =1.5–1.85 shows a short-ranged ferromagnetic correlation, and the on-site Coulomb interaction tends to strengthen ferromagnetic fluctuation sligh...

We study a model of interfacial crack in which contact of the crack faces obeys a Coulomb law of friction. For such cracks, the possibility that the stress has a stronger singularity than rÿ1=2 near the tip has been reported. In this paper, we demonstrate that these strong singularities can, in fact, be discarded, because they would assume a backward propagation of the crack. In passing, we pro...

Abstract: We study the non-factorizable corrections to W-pair-mediated four-fermion production in e+e− annihilation in double-pole approximation. We show how these corrections can be combined with the known corrections to the production and the decay of on-shell W-boson pairs, and how the full off-shell Coulomb singularity is included. Moreover, we find that the actual form of the real non-fact...

A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree-Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the "localized" and "delocalized" regions. A basis set for each region is combined to make a ne...

Much progress has been made in the last few decades in developing the necessary mathematics for understanding the full implications of the quantum-mechanical many-body problem and why the material world appears to be as stable as it is despite the serious −1/|x| singularity of the Coulomb potential that attracts negative electrons to positive atomic nuclei. Many problems remain, however, especi...

We describe electrical transport in ideal single-layer graphene at zero applied bias. There is a crossover from collisionless transport at frequencies larger than kBT/! (T is the temperature) to collision-dominated transport at lower frequencies. The d.c. conductivity is computed by the solution of a quantum Boltzmann equation. Due to a logarithmic singularity in the collinear scattering amplit...