4 research outputs found
A Unified Model for Two Localisation Problems: Electron States in Spin-Degenerate Landau Levels, and in a Random Magnetic Field
A single model is presented which represents both of the two apparently
unrelated localisation problems of the title. The phase diagram of this model
is examined using scaling ideas and numerical simulations. It is argued that
the localisation length in a spin-degenerate Landau level diverges at two
distinct energies, with the same critical behaviour as in a spin-split Landau
level, and that all states of a charged particle moving in two dimensions, in a
random magnetic field with zero average, are localised.Comment: 7 pages (RevTeX 3.0) plus 4 postscript figure
Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
We discuss different dualities of QHE in the framework of the noncommutative
Chern-Simons theory. First, we consider the Morita or T-duality transformation
on the torus which maps the abelian noncommutative CS description of QHE on the
torus into the nonabelian commutative description on the dual torus. It is
argued that the Ruijsenaars integrable many-body system provides the
description of the QHE with finite amount of electrons on the torus. The new
IIB brane picture for the QHE is suggested and applied to Jain and generalized
hierarchies. This picture naturally links 2d -model and 3d CS
description of the QHE. All duality transformations are identified in the brane
setup and can be related with the mirror symmetry and S duality. We suggest a
brane interpretation of the plateu transition in IQHE in which a critical point
is naturally described by WZW model.Comment: 31 pages, 4 figure
Dirichlet sigma models and mean curvature flow
The mean curvature flow describes the parabolic deformation of embedded
branes in Riemannian geometry driven by their extrinsic mean curvature vector,
which is typically associated to surface tension forces. It is the gradient
flow of the area functional, and, as such, it is naturally identified with the
boundary renormalization group equation of Dirichlet sigma models away from
conformality, to lowest order in perturbation theory. D-branes appear as fixed
points of this flow having conformally invariant boundary conditions. Simple
running solutions include the paper-clip and the hair-pin (or grim-reaper)
models on the plane, as well as scaling solutions associated to rational (p, q)
closed curves and the decay of two intersecting lines. Stability analysis is
performed in several cases while searching for transitions among different
brane configurations. The combination of Ricci with the mean curvature flow is
examined in detail together with several explicit examples of deforming curves
on curved backgrounds. Some general aspects of the mean curvature flow in
higher dimensional ambient spaces are also discussed and obtain consistent
truncations to lower dimensional systems. Selected physical applications are
mentioned in the text, including tachyon condensation in open string theory and
the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure