68,271 research outputs found
Magneto-Optical Stern-Gerlach Effect in Atomic Ensemble
We study the birefringence of the quantized polarized light in a
magneto-optically manipulated atomic ensemble as a generalized Stern-Gerlach
Effect of light. To explain this engineered birefringence microscopically, we
derive an effective Shr\"odinger equation for the spatial motion of two
orthogonally polarized components, which behave as a spin with an effective
magnetic moment leading to a Stern-Gerlach split in an nonuniform magnetic
field. We show that electromagnetic induced transparency (EIT) mechanism can
enhance the magneto-optical Stern-Gerlach effect of light in the presence of a
control field with a transverse spatial profile and a inhomogeneous magnetic
field.Comment: 7 pages, 5 figure
Wavelet Trees Meet Suffix Trees
We present an improved wavelet tree construction algorithm and discuss its
applications to a number of rank/select problems for integer keys and strings.
Given a string of length n over an alphabet of size , our
method builds the wavelet tree in time,
improving upon the state-of-the-art algorithm by a factor of .
As a consequence, given an array of n integers we can construct in time a data structure consisting of machine words and
capable of answering rank/select queries for the subranges of the array in
time. This is a -factor improvement in
query time compared to Chan and P\u{a}tra\c{s}cu and a -factor
improvement in construction time compared to Brodal et al.
Next, we switch to stringological context and propose a novel notion of
wavelet suffix trees. For a string w of length n, this data structure occupies
words, takes time to construct, and simultaneously
captures the combinatorial structure of substrings of w while enabling
efficient top-down traversal and binary search. In particular, with a wavelet
suffix tree we are able to answer in time the following two
natural analogues of rank/select queries for suffixes of substrings: for
substrings x and y of w count the number of suffixes of x that are
lexicographically smaller than y, and for a substring x of w and an integer k,
find the k-th lexicographically smallest suffix of x.
We further show that wavelet suffix trees allow to compute a
run-length-encoded Burrows-Wheeler transform of a substring x of w in time, where s denotes the length of the resulting run-length encoding.
This answers a question by Cormode and Muthukrishnan, who considered an
analogous problem for Lempel-Ziv compression.Comment: 33 pages, 5 figures; preliminary version published at SODA 201
From ten to four and back again: how to generalize the geometry
We discuss the four-dimensional N=1 effective approach in the study of warped
type II flux compactifications with SU(3)x SU(3)-structure to AdS_4 or flat
Minkowski space-time. The non-trivial warping makes it natural to use a
supergravity formulation invariant under local complexified Weyl
transformations. We obtain the classical superpotential from a standard
argument involving domain walls and generalized calibrations and show how the
resulting F-flatness and D-flatness equations exactly reproduce the full
ten-dimensional supersymmetry equations. Furthermore, we consider the effect of
non-perturbative corrections to this superpotential arising from gaugino
condensation or Euclidean D-brane instantons. For the latter we derive the
supersymmetry conditions in N=1 flux vacua in full generality. We find that the
non-perturbative corrections induce a quantum deformation of the internal
generalized geometry. Smeared instantons allow to understand KKLT-like AdS
vacua from a ten-dimensional point of view. On the other hand, non-smeared
instantons in IIB warped Calabi-Yau compactifications 'destabilize' the
Calabi-Yau complex structure into a genuine generalized complex one. This
deformation gives a geometrical explanation of the non-trivial superpotential
for mobile D3-branes induced by the non-perturbative corrections.Comment: LaTeX, 47 pages, v2, references, hyperref added, v3, correcting small
inaccuracies in eqs. (2.6a) and (5.16
Security of differential phase shift quantum key distribution against individual attacks
We derive a proof of security for the Differential Phase Shift Quantum Key
Distribution (DPSQKD) protocol under the assumption that Eve is restricted to
individual attacks. The security proof is derived by bounding the average
collision probability, which leads directly to a bound on Eve's mutual
information on the final key. The security proof applies to realistic sources
based on pulsed coherent light. We then compare individual attacks to
sequential attacks and show that individual attacks are more powerful
Blind Ptychographic Phase Retrieval via Convergent Alternating Direction Method of Multipliers
Ptychography has risen as a reference X-ray imaging technique: it achieves
resolutions of one billionth of a meter, macroscopic field of view, or the
capability to retrieve chemical or magnetic contrast, among other features. A
ptychographyic reconstruction is normally formulated as a blind phase retrieval
problem, where both the image (sample) and the probe (illumination) have to be
recovered from phaseless measured data. In this article we address a nonlinear
least squares model for the blind ptychography problem with constraints on the
image and the probe by maximum likelihood estimation of the Poisson noise
model. We formulate a variant model that incorporates the information of
phaseless measurements of the probe to eliminate possible artifacts. Next, we
propose a generalized alternating direction method of multipliers designed for
the proposed nonconvex models with convergence guarantee under mild conditions,
where their subproblems can be solved by fast element-wise operations.
Numerically, the proposed algorithm outperforms state-of-the-art algorithms in
both speed and image quality.Comment: 23 page
The Barrier Method: A Technique for Calculating Very Long Transition Times
In many dynamical systems there is a large separation of time scales between
typical events and "rare" events which can be the cases of interest. Rare-event
rates are quite difficult to compute numerically, but they are of considerable
practical importance in many fields: for example transition times in chemical
physics and extinction times in epidemiology can be very long, but are quite
important. We present a very fast numerical technique that can be used to find
long transition times (very small rates) in low-dimensional systems, even if
they lack detailed balance. We illustrate the method for a bistable
non-equilibrium system introduced by Maier and Stein and a two-dimensional (in
parameter space) epidemiology model.Comment: 20 pages, 8 figure
- …