9,285 research outputs found
Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence
We relate the intermittent fluctuations of velocity gradients in turbulence
to a whole range of local dissipation scales generalizing the picture of a
single mean dissipation length. The statistical distribution of these local
dissipation scales as a function of Reynolds number is determined in numerical
simulations of forced homogeneous isotropic turbulence with a spectral
resolution never applied before which exceeds the standard one by at least a
factor of eight. The core of the scale distribution agrees well with a
theoretical prediction. Increasing Reynolds number causes the generation of
ever finer local dissipation scales. This is in line with a less steep decay of
the large-wavenumber energy spectra in the dissipation range. The energy
spectrum for the highest accessible Taylor microscale Reynolds number
R_lambda=107 does not show a bottleneck.Comment: 8 pages, 5 figures (Figs. 1 and 3 in reduced quality
Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity
Let , , \int_{\tiny\mathbb{R}} J = 1 and
consider the nonlocal diffusion operator . We
study the equation , , in ,
where is a KPP-type nonlinearity, periodic in . We show that the
principal eigenvalue of the linearization around zero is well defined and that
a nontrivial solution of the nonlinear problem exists if and only if this
eigenvalue is negative. We prove that if, additionally, is symmetric, then
the nontrivial solution is unique
The problem of deficiency indices for discrete Schr\"odinger operators on locally finite graphs
The number of self-adjoint extensions of a symmetric operator acting on a
complex Hilbert space is characterized by its deficiency indices. Given a
locally finite unoriented simple tree, we prove that the deficiency indices of
any discrete Schr\"odinger operator are either null or infinite. We also prove
that almost surely, there is a tree such that all discrete Schr\"odinger
operators are essentially self-adjoint. Furthermore, we provide several
criteria of essential self-adjointness. We also adress some importance to the
case of the adjacency matrix and conjecture that, given a locally finite
unoriented simple graph, its the deficiency indices are either null or
infinite. Besides that, we consider some generalizations of trees and weighted
graphs.Comment: Typos corrected. References and ToC added. Paper slightly
reorganized. Section 3.2, about the diagonalization has been much improved.
The older section about the stability of the deficiency indices in now in
appendix. To appear in Journal of Mathematical Physic
Fast high-efficiency integrated waveguide photodetectors using novel hybrid vertical/butt coupling geometry
We report a novel coupling geometry for integrated waveguide photodetectors−a hybrid vertical coupling/butt coupling scheme that allows the integration of fast, efficient, photodetectors with conventional double heterostructure waveguides. It can be employed to yield a planar, or pseudo-planar, surface that supports further levels of integration. The approach is demonstrated with a 25-µm-long p-i-n detector integrated with an InP/InGaAsP/InP waveguide, which displays a high (~90%) efficiency and large (~15 GHz) bandwidth. This is the fastest high-efficiency integrated waveguide photodetector reported to date
Positivity of relative canonical bundles and applications
Given a family of canonically polarized manifolds, the
unique K\"ahler-Einstein metrics on the fibers induce a hermitian metric on the
relative canonical bundle . We use a global elliptic
equation to show that this metric is strictly positive on , unless
the family is infinitesimally trivial.
For degenerating families we show that the curvature form on the total space
can be extended as a (semi-)positive closed current. By fiber integration it
follows that the generalized Weil-Petersson form on the base possesses an
extension as a positive current. We prove an extension theorem for hermitian
line bundles, whose curvature forms have this property. This theorem can be
applied to a determinant line bundle associated to the relative canonical
bundle on the total space. As an application the quasi-projectivity of the
moduli space of canonically polarized varieties
follows.
The direct images , , carry natural hermitian metrics. We prove an
explicit formula for the curvature tensor of these direct images. We apply it
to the morphisms that are induced by the Kodaira-Spencer map and obtain a differential
geometric proof for hyperbolicity properties of .Comment: Supercedes arXiv:0808.3259v4 and arXiv:1002.4858v2. To appear in
Invent. mat
Quantum Communication Protocol Employing Weak Measurements
We propose a communication protocol exploiting correlations between two
events with a definite time-ordering: a) the outcome of a {\em weak
measurement} on a spin, and b) the outcome of a subsequent ordinary measurement
on the spin. In our protocol, Alice, first generates a "code" by performing
weak measurements on a sample of N spins.
The sample is sent to Bob, who later performs a post-selection by measuring
the spin along either of two certain directions. The results of the
post-selection define the "key', which he then broadcasts publicly. Using both
her previously generated code and this key, Alice is able to infer the {\em
direction} chosen by Bob in the post-selection. Alternatively, if Alice
broadcasts publicly her code, Bob is able to infer from the code and the key
the direction chosen by Alice for her weak measurement. Two possible
experimental realizations of the protocols are briefly mentioned.Comment: 5 pages, Revtex, 1 figure. A second protocol is added, where by a
similar set of weak measurement Alice can send, instead of receiving, a
message to Bob. The security question for the latter protocol is discusse
Spatially resolved ultrafast precessional magnetization reversal
Spatially resolved measurements of quasi-ballistic precessional magnetic
switching in a microstructure are presented. Crossing current wires allow
detailed study of the precessional switching induced by coincident longitudinal
and transverse magnetic field pulses. Though the response is initially
spatially uniform, dephasing occurs leading to nonuniformity and transient
demagnetization. This nonuniformity comes in spite of a novel method for
suppression of end domains in remanence. The results have implications for the
reliability of ballistic precessional switching in magnetic devices.Comment: 17 pages (including 4 figures), submitted to Phys. Rev. Let
Teleportation of Nonclassical Wave Packets of light
We report on the experimental quantum teleportation of strongly nonclassical
wave packets of light. To perform this full quantum operation while preserving
and retrieving the fragile non-classicality of the input state, we have
developed a broadband, zero-dispersion teleportation apparatus that works in
conjunction with time-resolved state preparation equipment. Our approach brings
within experimental reach a whole new set of hybrid protocols involving
discrete- and continuous-variable techniques in quantum information processing
for optical sciences
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