84 research outputs found
Disorder and Quantum Fluctuations in Superconducting Films in Strong Magnetic Fields
We find that the upper critical field in a two-dimensional disordered
superconductor can increase essentially at low temperatures. This happens due
to the formation of local superconducting islands weakly coupled via the
Josephson effect. The distribution of the superconducting islands is derived.
It is shown that the value of the critical field is determined by the interplay
of the proximity effect and quantum phase fluctuations. We find that the shift
of the upper critical field is connected with the pinning properties of a
superconductor.Comment: 4 page
Effect of screening of the Coulomb interaction on the conductivity in the quantum Hall regime
We study variable range hopping in the quantum Hall effect regime in the
presence of a metallic gate parallel to the plane of a two-dimensional electron
gas. Screening of the Coulomb interaction by the gate causes the partial
``filling'' of the Coulomb gap in the density of localized states. At low
enough temperatures this leads to a substantial enhancement and a new
temperature behavior of the hopping conductivity. As a result, the diagonal
conductivity peaks become much wider. The power law dependence of the width of
the peaks on the temperature changes: the corresponding exponent turns out to
be twice as small as that for gateless structures. The width dependences on the
current in non-ohmic regime and on the frequency for the absorption of the
electromagnetic waves experience a similar modification. The experimental
observation of the crossovers predicted may demonstrate the important role of
the Coulomb interaction in the integer quantum Hall regime.Comment: 14 pages + 3 figures by request preprint TPI-MINN-93/58-
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
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
Scaling Theory of the Integer Quantum Hall Effect
The scaling theory of the transitions between plateaus of the Hall
conductivity in the integer Quantum Hall effect is reviewed. In the model of
two-dimensional noninteracting electrons in strong magnetic fields the
transitions are disorder-induced localization-delocalization transitions. While
experimental and analytical approaches are surveyed, the main emphasis is on
numerical studies, which successfully describe the experiments. The theoretical
models for disordered systems are described in detail. An overview of the
finite-size scaling theory and its relation to Anderson localization is given.
The field-theoretical approach to the localization problem is outlined.
Numerical methods for the calculation of scaling quantities, in particular the
localization length, are detailed. The properties of local observables at the
localization-delocalization transition are discussed in terms of multifractal
measures. Finally, the results of extensive numerical investigations are
compared with experimental findings.Comment: 96 pages, REVTeX 3, 28 figures, Figs. 8-24, 26-28 appended as
uuencoded compressed tarred PostScript files. Submitted to Rev. Mod. Phys
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