Renormalization of QCD_2

The low energy infrared scaling of the multi-color 2-dimensional quantum chromodynamics is determined in the framework of its bosonized model by using the functional renormalization group method with gliding sharp cut-off k in momentum space in the local potential approximation. The model exhibits a single phase with a superuniversal effective potential.Comment: 15 pages, 3 figures, final versio

Ab-initio calculations of the optical properties of the Si(113)3x2ADI surface

We investigated the stable silicon (113) surface with a 3x2ADI reconstruction by ab-initio methods. The ground state properties have been obtained using the density-functional theory. We present the dispersion of the electronic band structure, where the surface bands have been distinguished from the projected bulk bands by calculating their localization in the slab. The optical spectra, here the reflectance anisotropy (RAS), have been obtained within the independent particle random phase approximation. We identified surface features in the spectra tracing them back to the responsible electronic states and, studied their localization in the slab. A comparison with available experimental data for the band structure and the RAS shows a good agreement.Comment: 10 pages, 10 figure

Variational approach to the scattering of charged particles by a many-electron system

We report a variational approach to the nonlinearly screened interaction of charged particles with a many-electron system. This approach has been developed by introducing a modification of the Schwinger variational principle of scattering theory, which allows to obtain nonperturbative scattering cross-sections of moving projectiles from the knowledge of the linear and quadratic density-response functions of the target. Our theory is illustrated with a calculation of the energy loss per unit path length of slow antiprotons moving in a uniform electron gas, which shows good agreement with a fully nonlinear self-consistent Hartree calculation. Since available self-consistent calculations are restricted to low heavy-projectile velocities, we expect our theory to have novel applications to a variety of processes where nonlinear screening plays an important role.Comment: 10 pages, 2 figures; Accepted to Physical Review

Numerical study of bound states for point charges shielded by the response of a homogeneous two-dimensional electron gas

We study numerically the existence and character of bound states for positive and negative point charges shielded by the response of a two-dimensional homogeneous electron gas. The problem is related to many physical situations and has recently arisen in experiments on impurities on metal surfaces with Shockley surface states. Mathematical theorems ascertain a bound state for two-dimensional circularly symmetric potentials V(r) with ∫∞0drrV(r)⩽0. We find that a shielded potential with ∫∞0drrV(r)>0 may also sustain a bound state. Moreover, on the same footing we study the electron-electron interactions in the two-dimensional electron gas, finding a bound state with an energy minimum for a certain electron gas density.Peer reviewe

Functional renormalization group with a compactly supported smooth regulator function

The functional renormalization group equation with a compactly supported smooth (CSS) regulator function is considered. It is demonstrated that in an appropriate limit the CSS regulator recovers the optimized one and it has derivatives of all orders. The more generalized form of the CSS regulator is shown to reduce to all major type of regulator functions (exponential, power-law) in appropriate limits. The CSS regulator function is tested by studying the critical behavior of the bosonized two-dimensional quantum electrodynamics in the local potential approximation and the sine-Gordon scalar theory for d<2 dimensions beyond the local potential approximation. It is shown that a similar smoothing problem in nuclear physics has already been solved by introducing the so called Salamon-Vertse potential which can be related to the CSS regulator.Comment: JHEP style, 11 pages, 2 figures, proofs corrected, accepted for publication by JHE