AMonte Carlo program for the simulation of four-fermion nal states at LEP2 is presented. It contains the Feynman diagrams with two resonating W's and Z's and features, among other things, initial and nal state radiation, Coulomb singularity e ects and e ective couplings. It is interfaced to the JETSET package to handle gluon radiation, hadronisation and decays. Its usefulness for experimental s...

A broad and a narrow level of a quantum dot connected to two external leads may swap their respective occupancies as a function of an external gate voltage. By mapping this problem onto a multiflavored Coulomb gas we show that such population switching is not abrupt. However, trying to measure it by adding a third electrostatically coupled lead may render this switching an abrupt first order qu...

When numerically solving the time-dependent Schrödinger equation for the electrons in an atom or molecule, the Coulomb singularity poses a challenge. The solution will have limited regularity, and high-order spatial discretisations, which are much favoured in the chemical physics community, are not performing to their full potential. By exploiting knowledge about the jumps in the derivatives of...

For a class of singular potentials, including the Coulomb potential and V (x) = g/x with the coefficient g in a certain range, 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 physical consequences depend seriously on the selfadjoint version chosen. The talk discusses ...

We extend the formulation of spin 2 fields on Minkowski space which makes the action manifestly invariant under duality rotations to the case of interactions with external electric and magnetic sources by adding suitable potentials for the longitudinal and trace parts. In this framework, the string singularity of the linearized Taub-NUT solution is resolved into a Coulomb-like solution. Suitabl...

We describe a new kind of transition between topologically distinct N = 2 type II Calabi–Yau vacua through points with enhanced non-abelian gauge symmetries together with fundamental charged matter hyper multiplets. We connect the appearance of matter to the local geometry of the singularity and discuss the relation between the instanton numbers of the Calabi–Yau manifolds taking part in the tr...

In this paper, we describe a new class of fast solvers for separable elliptic partial differential equations in cylindrical coordinates (r, θ, z) with free-space radiation conditions. By combining integral equation methods in the radial variable r with Fourier methods in θ and z, we show that high-order accuracy can be achieved in both the governing potential and its derivatives. A weak singula...

Current steps attributed to resonant tunneling through individual InAs quantum dots embedded in a GaAs-AlAs-GaAs tunneling device are investigated experimentally in magnetic fields up to 28 T. The steps evolve into strongly enhanced current peaks in high fields. This can be understood as a fieldinduced Fermi-edge singularity due to the Coulomb interaction between the tunneling electron on the q...

We prove a quantitative and global in time semiclassical limit from the Hartree to Vlasov equation case of singular interaction potential dimension $d\geq 3$, including Coulomb singularity $d=3$. This result holds for initial data concentrated enough sense that some space moments are initially sufficiently small. As an intermediate result, we also obtain bounds on velocity even order asymptotic...