1,822 research outputs found
A family of sure-success quantum algorithms for solving a generalized Grover search problem
This work considers a generalization of Grover's search problem, viz., to
find any one element in a set of acceptable choices which constitute a fraction
f of the total number of choices in an unsorted data base. An infinite family
of sure-success quantum algorithms are introduced here to solve this problem,
each member for a different range of f. The nth member of this family involves
n queries of the data base, and so the lowest few members of this family should
be very convenient algorithms within their ranges of validity. The even member
{A}_{2n} of the family covers ever larger range of f for larger n, which is
expected to become the full range 0 infinity.Comment: 8 pages, including 4 figures in 4 page
Geometry, thermodynamics, and finite-size corrections in the critical Potts model
We establish an intriguing connection between geometry and thermodynamics in
the critical q-state Potts model on two-dimensional lattices, using the q-state
bond-correlated percolation model (QBCPM) representation. We find that the
number of clusters of the QBCPM has an energy-like singularity for q different
from 1, which is reached and supported by exact results, numerical simulation,
and scaling arguments. We also establish that the finite-size correction to the
number of bonds, has no constant term and explains the divergence of related
quantities as q --> 4, the multicritical point. Similar analyses are applicable
to a variety of other systems.Comment: 12 pages, 6 figure
Demonstration of fundamental mode only propagation in highly multimode fibre for high power EDFAs
The use of short lengths of large core phosphate glass fibre, doped with high
concentrations of Er or Er:Yb represents an attractive route to achieving high
power erbium doped fibre amplifiers (EDFAs) and lasers (EDFLs). With the aim of
investigating the potential of achieving diffraction limited output from such
large core fibres, we present experimental results of fundamental mode
propagation through a 20 cm length of passive 300 micrometer core multimode
fibre when the input is a well-aligned Gaussian beam. Through careful control
of fibre geometry, input beam parameters and alignment, we measured an output M
squared of 1.1 + - 0.05. The fibre had a numerical aperture of 0.389, implying
a V number of 236.8. To our knowledge, this is the largest core fibre through
which diffraction limited fundamental mode propagation has been demonstrated.
Although the results presented here relate to undoped fibre, they do provide
the practical basis for a new generation of EDFAs and EDFLs.Comment: 5 figure
Electronic Structure of Multiple Dots
We calculate, via spin density functional theory (SDFT) and exact
diagonalization, the eigenstates for electrons in a variety of external
potentials, including double and triple dots. The SDFT calculations employ
realistic wafer profiles and gate geometries and also serve as the basis for
the exact diagonalization calculations. The exchange interaction J between
electrons is the difference between singlet and triplet ground state energies
and reflects competition between tunneling and the exchange matrix element,
both of which result from overlap in the barrier. For double dots, a
characteristic transition from singlet ground state to triplet ground state
(positive to negative J) is calculated. For the triple dot geometry with 2
electrons we also find the electronic structure with exact diagonalization. For
larger electron number (18 and 20) we use only SDFT. In contrast to the double
dot case, the triple dot case shows a quasi-periodic fluctuation of J with
magnetic field which we attribute to periodic variations of the basis states in
response to changing flux quanta threading the triple dot structure.Comment: 3 pages, 4 figure
Percolation on two- and three-dimensional lattices
In this work we apply a highly efficient Monte Carlo algorithm recently
proposed by Newman and Ziff to treat percolation problems. The site and bond
percolation are studied on a number of lattices in two and three dimensions.
Quite good results for the wrapping probabilities, correlation length critical
exponent and critical concentration are obtained for the square, simple cubic,
HCP and hexagonal lattices by using relatively small systems. We also confirm
the universal aspect of the wrapping probabilities regarding site and bond
dilution.Comment: 15 pages, 6 figures, 3 table
Fluctuations of an evaporating black hole from back reaction of its Hawking radiation: Questioning a premise in earlier work
This paper delineates the first steps in a systematic quantitative study of
the spacetime fluctuations induced by quantum fields in an evaporating black
hole. We explain how the stochastic gravity formalism can be a useful tool for
that purpose within a low-energy effective field theory approach to quantum
gravity. As an explicit example we apply it to the study of the
spherically-symmetric sector of metric perturbations around an evaporating
black hole background geometry. For macroscopic black holes we find that those
fluctuations grow and eventually become important when considering sufficiently
long periods of time (of the order of the evaporation time), but well before
the Planckian regime is reached. In addition, the assumption of a simple
correlation between the fluctuations of the energy flux crossing the horizon
and far from it, which was made in earlier work on spherically-symmetric
induced fluctuations, is carefully analyzed and found to be invalid. Our
analysis suggests the existence of an infinite amplitude for the fluctuations
of the horizon as a three-dimensional hypersurface. We emphasize the need for
understanding and designing operational ways of probing quantum metric
fluctuations near the horizon and extracting physically meaningful information.Comment: 10 pages, REVTeX; minor changes, a few references added and a brief
discussion of their relevance included. To appear in the proceedings of the
10th Peyresq meeting. Dedicated to Rafael Sorkin on the occasion of his 60th
birthda
Universality of the Crossing Probability for the Potts Model for q=1,2,3,4
The universality of the crossing probability of a system to
percolate only in the horizontal direction, was investigated numerically by
using a cluster Monte-Carlo algorithm for the -state Potts model for
and for percolation . We check the percolation through
Fortuin-Kasteleyn clusters near the critical point on the square lattice by
using representation of the Potts model as the correlated site-bond percolation
model. It was shown that probability of a system to percolate only in the
horizontal direction has universal form for
as a function of the scaling variable . Here,
is the probability of a bond to be closed, is the
nonuniversal crossing amplitude, is the nonuniversal metric factor,
is the nonuniversal scaling index, is the correlation
length index.
The universal function . Nonuniversal scaling factors
were found numerically.Comment: 15 pages, 3 figures, revtex4b, (minor errors in text fixed,
journal-ref added
Wavy stripes and squares in zero P number convection
A simple model to explain numerically observed behaviour of chaotically
varying stripes and square patterns in zero Prandtl number convection in
Boussinesq fluid is presented. The nonlinear interaction of mutually
perpendicular sets of wavy rolls, via higher mode, may lead to a competition
between the two sets of wavy rolls. The appearance of square patterns is due to
the secondary forward Hopf bifurcation of a set of wavy rolls.Comment: 8 pages and 3 figures, late
On the energy leakage of discrete wavelet transform
The energy leakage is an inherent deficiency of discrete wavelet transform (DWT) which is often ignored by researchers and practitioners. In this paper, a systematic investigation into the energy leakage is reported. The DWT is briefly introduced first, and then the energy leakage phenomenon is described using a numerical example as an illustration and its effect on the DWT results is discussed. Focusing on the Daubechies wavelet functions, the band overlap between the quadrature mirror analysis filters was studied and the results reveal that there is an unavoidable tradeoff between the band overlap degree and the time resolution for the DWT. The dependency of the energy leakage to the wavelet function order was studied by using a criterion defined to evaluate the severity of the energy leakage. In addition, a method based on resampling technique was proposed to relieve the effects of the energy leakage. The effectiveness of the proposed method has been validated by numerical simulation study and experimental study
Low-Loss All-Optical Zeno Switch in a Microdisk Cavity Using EIT
We present theoretical results of a low-loss all-optical switch based on
electromagnetically induced transparency and the classical Zeno effect in a
microdisk resonator. We show that a control beam can modify the atomic
absorption of the evanescent field which suppresses the cavity field buildup
and alters the path of a weak signal beam. We predict more than 35 dB of
switching contrast with less than 0.1 dB loss using just 2 micro-Watts of
control-beam power for signal beams with less than single photon intensities
inside the cavity.Comment: Updated with new references, corrected Eq 2a, and added introductory
text. 7 pages, 5 figures, 3 table
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