13,775 research outputs found
Deterministic creation, pinning, and manipulation of quantized vortices in a Bose-Einstein condensate
We experimentally and numerically demonstrate deterministic creation and
manipulation of a pair of oppositely charged singly quantized vortices in a
highly oblate Bose-Einstein condensate (BEC). Two identical blue-detuned,
focused Gaussian laser beams that pierce the BEC serve as repulsive obstacles
for the superfluid atomic gas; by controlling the positions of the beams within
the plane of the BEC, superfluid flow is deterministically established around
each beam such that two vortices of opposite circulation are generated by the
motion of the beams, with each vortex pinned to the \emph{in situ} position of
a laser beam. We study the vortex creation process, and show that the vortices
can be moved about within the BEC by translating the positions of the laser
beams. This technique can serve as a building block in future experimental
techniques to create, on-demand, deterministic arrangements of few or many
vortices within a BEC for precise studies of vortex dynamics and vortex
interactions.Comment: 9 pages, 7 figure
Quantum nanophotonics using hyperbolic metamaterials
Engineering the optical properties using artificial nanostructured media
known as metamaterials has led to breakthrough devices with capabilities from
super-resolution imaging to invisibility. In this article, we review
metamaterials for quantum nanophotonic applications, a recent development in
the field. This seeks to address many challenges in the field of quantum optics
using recent advances in nanophotonics and nanofabrication. We focus on the
class of nanostructured media with hyperbolic dispersion that have emerged as
one of the most promising metamaterials with a multitude of practical
applications from subwavelength imaging, nanoscale waveguiding, biosensing to
nonlinear switching. We present the various design and characterization
principles of hyperbolic metamaterials and explain the most important property
of such media: a broadband enhancement in the electromagnetic density of
states. We review several recent experiments that have explored this phenomenon
using spontaneous emission from dye molecules and quantum dots. We finally
point to future applications of hyperbolic metamaterials of using the broadband
enhancement in the spontaneous emission to construct single photon sources.Comment: 25 pages, 12 figures, Review Articl
Exact eigenvalue spectrum of a class of fractal scale-free networks
The eigenvalue spectrum of the transition matrix of a network encodes
important information about its structural and dynamical properties. We study
the transition matrix of a family of fractal scale-free networks and
analytically determine all the eigenvalues and their degeneracies. We then use
these eigenvalues to evaluate the closed-form solution to the eigentime for
random walks on the networks under consideration. Through the connection
between the spectrum of transition matrix and the number of spanning trees, we
corroborate the obtained eigenvalues and their multiplicities.Comment: Definitive version accepted for publication in EPL (Europhysics
Letters
An Exact No Free Lunch Theorem for Community Detection
A precondition for a No Free Lunch theorem is evaluation with a loss function
which does not assume a priori superiority of some outputs over others. A
previous result for community detection by Peel et al. (2017) relies on a
mismatch between the loss function and the problem domain. The loss function
computes an expectation over only a subset of the universe of possible outputs;
thus, it is only asymptotically appropriate with respect to the problem size.
By using the correct random model for the problem domain, we provide a
stronger, exact No Free Lunch theorem for community detection. The claim
generalizes to other set-partitioning tasks including core/periphery
separation, -clustering, and graph partitioning. Finally, we review the
literature of proposed evaluation functions and identify functions which
(perhaps with slight modifications) are compatible with an exact No Free Lunch
theorem
Lyapunov exponents for products of complex Gaussian random matrices
The exact value of the Lyapunov exponents for the random matrix product with each , where
is a fixed positive definite matrix and a complex Gaussian matrix with entries standard complex normals, are
calculated. Also obtained is an exact expression for the sum of the Lyapunov
exponents in both the complex and real cases, and the Lyapunov exponents for
diffusing complex matrices.Comment: 15 page
Restrictions and Stability of Time-Delayed Dynamical Networks
This paper deals with the global stability of time-delayed dynamical
networks. We show that for a time-delayed dynamical network with
non-distributed delays the network and the corresponding non-delayed network
are both either globally stable or unstable. We demonstrate that this may not
be the case if the network's delays are distributed. The main tool in our
analysis is a new procedure of dynamical network restrictions. This procedure
is useful in that it allows for improved estimates of a dynamical network's
global stability. Moreover, it is a computationally simpler and much more
effective means of analyzing the stability of dynamical networks than the
procedure of isospectral network expansions introduced in [Isospectral graph
transformations, spectral equivalence, and global stability of dynamical
networks. Nonlinearity, 25 (2012) 211-254]. The effectiveness of our approach
is illustrated by applications to various classes of Cohen-Grossberg neural
networks.Comment: 32 pages, 9 figure
Diffusive persistence and the `sign-time' distribution
We present a new method for extracting the persistence exponent theta for the
diffusion equation, based on the distribution P of `sign-times'. With the aid
of a numerically verified Ansatz for P we derive an exact formula for theta in
arbitrary spatial dimension d. Our results are in excellent agreement with
previous numerical studies. Furthermore, our results indicate a qualitative
change in P above d ~ 36, signalling the existence of a sharp change in the
ergodic properties of the diffusion field.Comment: 5 pages, 2 tar gzip figures (Latex), subm. to PRE (Rapid Comm), new
reference adde
Development of the 'SNS Older Adults measure' (SNS-OA) to examine social network site use in older adults
Objectives: Social Networking Sites (SNSs) may ameliorate loneliness in later life but no measure of SNS use for this population exists. This study describes the development of the ‘SNS Older Adults measure’ (SNS-OA), to improve understanding of older adults’ SNS use and its relationship to social wellbeing. /
Methods: The SNS-OA underwent initial development, including literature reviews and consultation with target population (n = 9) and experts (n = 9); piloting (n = 74), and evaluation of psychometric properties (n = 263). /
Results: The final measure comprised three ‘motive’ scales (using SNSs to maintain close ties, maintain and strengthen weaker ties and diversion), and two ‘affect’ scales (positive/negative). Whilst many items were weakly endorsed by participants, the measure demonstrated good reliability (Cronbach α = 0.85; ICC = 0.82) and some convergent validity, with some subscales correlating with a personality measure in hypothesised directions. No statistically significant correlations were observed between the measure and social wellbeing. /
Conclusions: Despite the measure’s limitations, this research has enabled a better understanding of SNS use in older adults and has important implications for research in this area. Findings also suggest a complex relationship between social wellbeing and SNS use in later life
Statistical mechanics of topological phase transitions in networks
We provide a phenomenological theory for topological transitions in
restructuring networks. In this statistical mechanical approach energy is
assigned to the different network topologies and temperature is used as a
quantity referring to the level of noise during the rewiring of the edges. The
associated microscopic dynamics satisfies the detailed balance condition and is
equivalent to a lattice gas model on the edge-dual graph of a fully connected
network. In our studies -- based on an exact enumeration method, Monte-Carlo
simulations, and theoretical considerations -- we find a rich variety of
topological phase transitions when the temperature is varied. These transitions
signal singular changes in the essential features of the global structure of
the network. Depending on the energy function chosen, the observed transitions
can be best monitored using the order parameters Phi_s=s_{max}/M, i.e., the
size of the largest connected component divided by the number of edges, or
Phi_k=k_{max}/M, the largest degree in the network divided by the number of
edges. If, for example the energy is chosen to be E=-s_{max}, the observed
transition is analogous to the percolation phase transition of random graphs.
For this choice of the energy, the phase-diagram in the [,T] plane is
constructed. Single vertex energies of the form
E=sum_i f(k_i), where k_i is the degree of vertex i, are also studied.
Depending on the form of f(k_i), first order and continuous phase transitions
can be observed. In case of f(k_i)=-(k_i+c)ln(k_i), the transition is
continuous, and at the critical temperature scale-free graphs can be recovered.Comment: 12 pages, 12 figures, minor changes, added a new refernce, to appear
in PR
Hawking Radiation of Dirac Particles in an Arbitrarily Accelerating Kinnersley Black Hole
Quantum thermal effect of Dirac particles in an arbitrarily accelerating
Kinnersley black hole is investigated by using the method of generalized
tortoise coordinate transformation. Both the location and the temperature of
the event horizon depend on the advanced time and the angles. The Hawking
thermal radiation spectrum of Dirac particles contains a new term which
represents the interaction between particles with spin and black holes with
acceleration. This spin-acceleration coupling effect is absent from the thermal
radiation spectrum of scalar particles.Comment: Revtex, 12pt, 16 pages, no figure, to appear in Gen. Rel. Grav. 34
(2002) N0.
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