2,899 research outputs found
-integrability, dimensions of supports of fourier transforms and applications
It is proved that there does not exist any non zero function in
with if its Fourier transform is supported by a set of
finite packing -measure where . It is shown that the
assertion fails for . The result is applied to prove
Wiener-Tauberian theorems for and M(2)
Fourier asymptotics, Hardy type inequality and fractal measures
Suppose is an -dimensional fractal measure for some
. Inspired by the results proved by R. Strichartz in 1990, we
discuss the -asymptotics of the Fourier transform of by estimating
bounds of
for and . In a
different direction, we prove a Hardy type inequality, that is,
where and
for
generalizing the one dimensional results proved by
Hudson and Leckband in 1992
Sharp weighted estimates for multi-frequency Calder\'on-Zygmund operators
In this paper we study weighted estimates for the multi-frequency
Calder\'{o}n-Zygmund operators associated with the frequency set
and modulus of continuity
satisfying the usual Dini condition. We use the modern method of domination by
sparse operators and obtain bounds for the exponents of and characteristic
Superfluid Insulator Transitions of Hard-Core Bosons on the Checkerboard Lattice
We study hard-core bosons on the checkerboard lattice with nearest neighbour
unfrustrated hopping and `tetrahedral' plaquette charging energy .
Analytical arguments and Quantum Monte Carlo simulations lead us to the
conclusion that the system undergoes a zero temperature () quantum phase
transition from a superfluid phase at small to a large Mott
insulator phase with = 1/4 for a range of values of the chemical
potential . Further, the quarter-filled insulator breaks lattice
translation symmetry in a characteristic four-fold ordering pattern, and
occupies a lobe of finite extent in the - phase diagram. A Quantum
Monte-Carlo study slightly away from the tip of the lobe provides evidence for
a direct weakly first-order superfluid-insulator transition away from the tip
of the lobe. While analytical arguments leads us to conclude that the
transition {\em at} the tip of the lobe belongs to a different landau-forbidden
second-order universality class, an extrapolation of our numerical results
suggests that the size of the first-order jump does not go to zero even at the
tip of the lobe.Comment: published versio
Detecting fractions of electrons in the high- cuprates
We propose several tests of the idea that the electron is fractionalized in
the underdoped and undoped cuprates. These include the ac Josephson effect, and
tunneling into small superconducting grains in the Coulomb blockade regime. In
both cases, we argue that the results are qualitatively modified from the
conventional ones if the insulating tunnel barrier is fractionalized. These
experiments directly detect the possible existence of the chargon - a charge
spinless boson - in the insulator. The effects described in this paper
provide a means to probing whether the undoped cuprate (despite it's magnetism)
is fractionalized. Thus, the experiments discussed here are complementary to
the flux-trapping experiment we proposed in our earlier work(cond-mat/0006481).Comment: 7 pages, 5 figure
Fermi surfaces in general co-dimension and a new controlled non-trivial fixed point
Traditionally Fermi surfaces for problems in spatial dimensions have
dimensionality , i.e., codimension along which energy varies.
Situations with arise when the gapless fermionic excitations live at
isolated nodal points or lines. For weak short range interactions are
irrelevant at the non-interacting fixed point. Increasing interaction strength
can lead to phase transitions out of this Fermi liquid. We illustrate this by
studying the transition to superconductivity in a controlled
expansion near . The resulting non-trivial fixed point is shown to
describe a scale invariant theory that lives in effective space-time dimension
. Remarkably, the results can be reproduced by the more familiar
Hertz-Millis action for the bosonic superconducting order parameter even though
it lives in different space-time dimensions.Comment: 4 page
Majorana spin liquids and projective realization of SU(2) spin symmetry
We revisit the fermionic parton approach to S = 1/2 quantum spin liquids with
SU(2) spin rotation symmetry, and the associated projective symmetry group
(PSG) classification. We point out that the existing PSG classification is
incomplete; upon completing it, we find spin liquid states with S=1 and S=0
Majorana fermion excitations coupled to a deconfined Z2 gauge field. The
crucial observation leading us to this result is that, like space group and
time reversal symmetries, spin rotations can act projectively on the fermionic
partons; that is, a spin rotation may be realized by simultaneous SU(2) spin
and gauge rotations. We show that there are only two realizations of spin
rotations acting on fermionic partons: the familiar naive realization where
spin rotation is not accompanied by any gauge transformation, and a single type
of projective realization. We discuss the PSG classification for states with
projective spin rotations. To illustrate these results, we show that there are
four such PSGs on the two-dimensional square lattice. We study the properties
of the corresponding states, finding that one -- with gapless Fermi points --
is a stable phase beyond mean-field theory. In this phase, depending on
parameters, a small Zeeman magnetic field can open a partial gap for the
Majorana fermion excitations. Moreover, there are nearby gapped phases
supporting Z2 vortex excitations obeying non-Abelian statistics. We conclude
with a discussion of various open issues, including the challenging question of
where such S=1 Majorana spin liquids may occur in models and in real systems.Comment: 19 pages, 8 figures. Typos corrected, references adde
A smart material based approach to morphing
This presentation gives an overview of the Shape Memory Alloy (SMA) based approach to the research and13; development of adaptive/smart/morphing airframe structural technologies at the Advanced Composites13; Division, NAL. Central to this approach is the efficient integration of thermal NiTi SMA elements with13; polymeric carbon composites. The SMA elements could be either externally placed or embedded in the13; polymeric composite. The external connection could be in the form of mechanisms / devices
- …