175 research outputs found
An Infrared study of the Josephson vortex state in high-Tc cuprates
We report the results of the c-axis infrared spectroscopy of La_{2-x} Sr_x
CuO_4 in high magnetic field oriented parallel to the CuO_2 planes. A
significant suppression of the superfluid density with magnetic field rho_s(H)
is observed for both underdoped (x=0.125) and overdoped (x=0.17) samples. We
show that the existing theoretical models of the Josephson vortex state fail to
consistently describe the observed effects and discuss possible reasons for the
discrepancies
New Josephson Plasma Modes in Underdoped YBa2Cu3O6.6 Induced by Parallel Magnetic Field
The c-axis reflectivity spectrum of underdoped YBa2Cu3O6.6 (YBCO) is measured
below Tc=59K in parallel magnetic fields H//CuO2 up to 7T. Upon application of
a parallel field, a new peak appears at finite frequency in the optical
conductivity at the expense of suppression of c-axis condensate weight. We
conclude that the dramatic change originates from different Josephson coupling
strengths between bilayers with and without Josephson vortices. We find that
the 400cm^-1 broad conductivity peak in YBCO gains the spectral weight under
parallel magnetic field; this indicates that the condensate weight at \omega =0
is distributed to the intra-bilayer mode as well as to the new optical
Josephson mode.Comment: 4 pages, 3 figure
A Generalization of the Convex Kakeya Problem
Given a set of line segments in the plane, not necessarily finite, what is a
convex region of smallest area that contains a translate of each input segment?
This question can be seen as a generalization of Kakeya's problem of finding a
convex region of smallest area such that a needle can be rotated through 360
degrees within this region. We show that there is always an optimal region that
is a triangle, and we give an optimal \Theta(n log n)-time algorithm to compute
such a triangle for a given set of n segments. We also show that, if the goal
is to minimize the perimeter of the region instead of its area, then placing
the segments with their midpoint at the origin and taking their convex hull
results in an optimal solution. Finally, we show that for any compact convex
figure G, the smallest enclosing disk of G is a smallest-perimeter region
containing a translate of every rotated copy of G.Comment: 14 pages, 9 figure
Lines Missing Every Random Point
We prove that there is, in every direction in Euclidean space, a line that
misses every computably random point. We also prove that there exist, in every
direction in Euclidean space, arbitrarily long line segments missing every
double exponential time random point.Comment: Added a section: "Betting in Doubly Exponential Time.
Stochastic transitions of attractors in associative memory models with correlated noise
We investigate dynamics of recurrent neural networks with correlated noise to
analyze the noise's effect. The mechanism of correlated firing has been
analyzed in various models, but its functional roles have not been discussed in
sufficient detail. Aoyagi and Aoki have shown that the state transition of a
network is invoked by synchronous spikes. We introduce two types of noise to
each neuron: thermal independent noise and correlated noise. Due to the effects
of correlated noise, the correlation between neural inputs cannot be ignored,
so the behavior of the network has sample dependence. We discuss two types of
associative memory models: one with auto- and weak cross-correlation
connections and one with hierarchically correlated patterns. The former is
similar in structure to Aoyagi and Aoki's model. We show that stochastic
transition can be presented by correlated rather than thermal noise. In the
latter, we show stochastic transition from a memory state to a mixture state
using correlated noise. To analyze the stochastic transitions, we derive a
macroscopic dynamic description as a recurrence relation form of a probability
density function when the correlated noise exists. Computer simulations agree
with theoretical results.Comment: 21 page
Josephson Coupling, Phase Correlations, and Josephson Plasma Resonance in Vortex Liquid Phase
Josephson plasma resonance has been introduced recently as a powerful tool to
probe interlayer Josephson coupling in different regions of the vortex phase
diagram in layered superconductors. In the liquid phase, the high temperature
expansion with respect to the Josephson coupling connects the Josephson plasma
frequency with the phase correlation function. This function, in turn, is
directly related to the pair distribution function of the liquid. We develop a
recipe to extract the phase and density correlation functions from the
dependencies of the plasma resonance frequency and the
axis conductivity on the {\it ab}-component of the
magnetic field at fixed {\it c} -component. Using Langevin dynamic simulations
of two-dimensional vortex arrays we calculate density and phase correlation
functions at different temperatures. Calculated phase correlations describe
very well the experimental angular dependence of the plasma resonance field. We
also demonstrate that in the case of weak damping in the liquid phase,
broadening of the JPR line is caused mainly by random Josephson coupling
arising from the density fluctuations of pancake vortices. In this case the JPR
line has a universal shape, which is determined only by parameters of the
superconductors and temperature.Comment: 22 pages, 6 figures, to appear in Phys. Rev. B, December
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