99 research outputs found
Tail states in superconductors with weak magnetic impurities
We analyse the behavior of the density of states in a singlet s-wave
superconductor with weak magnetic impurities in the clean limit by using the
method of optimal fluctuation. We show that the density of states varies as
near the mean field gap edge
in a d-dimensional superconductor. The optimal fluctuation in d>1 is
strongly anisotropic. We compare the density of states with that obtained in
other recent approaches.Comment: 2 pages, to appear in Proceedings of LT-23; (v2) some affiliations
change
Conductance and its universal fluctuations in the directed network model at the crossover to the quasi-one-dimensional regime
The directed network model describing chiral edge states on the surface of a
cylindrical 3D quantum Hall system is known to map to a one-dimensional quantum
ferromagnetic spin chain. Using the spin wave expansion for this chain, we
determine the universal functions for the crossovers between the 2D chiral
metallic and 1D metallic regimes in the mean and variance of the conductance
along the cylinder, to first nontrivial order.Comment: 10 pages, REVTeX, uses epsf, 2 .eps figures included. Newly written
Introduction and small changes to other section
Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class
We study the multifractality (MF) of critical wave functions at boundaries
and corners at the metal-insulator transition (MIT) for noninteracting
electrons in the two-dimensional (2D) spin-orbit (symplectic) universality
class. We find that the MF exponents near a boundary are different from those
in the bulk. The exponents at a corner are found to be directly related to
those at a straight boundary through a relation arising from conformal
invariance. This provides direct numerical evidence for conformal invariance at
the 2D spin-orbit MIT. The presence of boundaries modifies the MF of the whole
sample even in the thermodynamic limit.Comment: 5 pages, 4 figure
Global properties of Stochastic Loewner evolution driven by Levy processes
Standard Schramm-Loewner evolution (SLE) is driven by a continuous Brownian
motion which then produces a trace, a continuous fractal curve connecting the
singular points of the motion. If jumps are added to the driving function, the
trace branches. In a recent publication [1] we introduced a generalized SLE
driven by a superposition of a Brownian motion and a fractal set of jumps
(technically a stable L\'evy process). We then discussed the small-scale
properties of the resulting L\'evy-SLE growth process. Here we discuss the same
model, but focus on the global scaling behavior which ensues as time goes to
infinity. This limiting behavior is independent of the Brownian forcing and
depends upon only a single parameter, , which defines the shape of the
stable L\'evy distribution. We learn about this behavior by studying a
Fokker-Planck equation which gives the probability distribution for endpoints
of the trace as a function of time. As in the short-time case previously
studied, we observe that the properties of this growth process change
qualitatively and singularly at . We show both analytically and
numerically that the growth continues indefinitely in the vertical direction
for , goes as for , and saturates for . The probability density has two different scales corresponding to
directions along and perpendicular to the boundary. In the former case, the
characteristic scale is . In the latter case the scale
is for , and
for . Scaling functions for the probability density are given for
various limiting cases.Comment: Published versio
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