404 research outputs found
Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup
For an affine spherical homogeneous space G/H of a connected semisimple
algebraic group G, we consider the factorization morphism by the action on G/H
of a maximal unipotent subgroup of G. We prove that this morphism is
equidimensional if and only if the weight semigroup of G/H satisfies some
simple condition.Comment: v2: title and abstract changed; v3: 16 pages, minor correction
Difficulties of an Infrared Extension of Differential Renormalization
We investigate the possibility of generalizing differential renormalization
of D.Z.Freedman, K.Johnson and J.I.Latorre in an invariant fashion to theories
with infrared divergencies via an infrared operation.
Two-dimensional models and the four-dimensional theory
diagrams with exceptional momenta are used as examples, while dimensional
renormalization serves as a test scheme for comparison. We write the basic
differential identities of the method simultaneously in co-ordinate and
momentum space, introducing two scales which remove ultraviolet and infrared
singularities. The consistent set of Fourier-transformation formulae is
derived. However, the values for tadpole-type Feynman integrals in higher
orders of perturbation theory prove to be ambiguous, depending on the order of
evaluation of the subgraphs. In two dimensions, even earlier than this
ambiguity manifests itself, renormalization-group calculations based on
infrared extension of differential renormalization lead to incorrect results.
We conclude that the extended differential renormalization procedure does not
perform the infrared operation in a self-consistent way, as the
original recipe does the ultraviolet operation.Comment: (minor changes have been made to make clear that no infrared problems
occur in the original ultraviolet procedure of [1]; subsection 2.1 has been
added to outline the ideas a simple example), 26 pages, LaTeX, JINR preprint
E2-92-538, Dubna (Dec.1992
Electron Spin Dynamics of the Superconductor CaC6 probed by ESR
Conduction Electron Spin Resonance (CESR) was measured on a thick slab of
CaC6 in the normal and superconducting state. A surprising increase of the CESR
intensity below Tc can not be explained by the theoretically predicted change
in spin susceptibility. It is interpreted as a vortex enhanced increase of the
effective skin depth. Non-linear microwave absorption measurements in the
superconducting state describe CaC6 as an anisotropic BCS superconductor. The
study of the spin dynamics in the superconducting state and the discovery of
the vortex enhanced increase of the skin depth poses a challenge to theory to
provide a comprehensive description of the observed phenomena. CESR data in the
normal state characterize CaC6 as a three-dimensional (3D) metal. The analysis
suggests that the scattering of conduction electrons is dominated by impurities
and supports the description of superconductivity in the dirty limit.Comment: 4 pages, 3 figure
Transcendental numbers and the topology of three-loop bubbles
We present a proof that all transcendental numbers that are needed for the
calculation of the master integrals for three-loop vacuum Feynman diagrams can
be obtained by calculating diagrams with an even simpler topology, the topology
of spectacles.Comment: 4 pages in REVTeX, 1 PostScript figure included, submitted to Phys.
Rev. Let
Variational approach for electrolyte solutions: from dielectric interfaces to charged nanopores
A variational theory is developed to study electrolyte solutions, composed of
interacting point-like ions in a solvent, in the presence of dielectric
discontinuities and charges at the boundaries. Three important and non-linear
electrostatic effects induced by these interfaces are taken into account:
surface charge induced electrostatic field, solvation energies due to the ionic
cloud, and image charge repulsion. Our variational equations thus go beyond the
mean-field theory. The influence of salt concentration, ion valency, dielectric
jumps, and surface charge is studied in two geometries. i) A single neutral
air-water interface with an asymmetric electrolyte. A charge separation and
thus an electrostatic field gets established due to the different image charge
repulsions for coions and counterions. Both charge distributions and surface
tension are computed and compared to previous approximate calculations. For
symmetric electrolyte solutions close to a charged surface, two zones are
characterized. In the first one, with size proportional to the logarithm of the
coupling parameter, strong image forces impose a total ion exclusion, while in
the second zone the mean-field approach applies. ii) A symmetric electrolyte
confined between two dielectric interfaces as a simple model of ion rejection
from nanopores. The competition between image charge repulsion and attraction
of counterions by the membrane charge is studied. For small surface charge, the
counterion partition coefficient decreases with increasing pore size up to a
critical pore size, contrary to neutral membranes. For larger pore sizes, the
whole system behaves like a neutral pore. The prediction of the variational
method is also compared with MC simulations and a good agreement is observed.Comment: This version is accepted for publication in Phys. Rev. E
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