183,231 research outputs found
Quantizing Strings in de Sitter Space
We quantize a string in the de Sitter background, and we find that the mass
spectrum is modified by a term which is quadratic in oscillating numbers, and
also proportional to the square of the Hubble constant.Comment: 13 pages. Version published in JHE
On the All-Speed Roe-type Scheme for Large Eddy Simulation of Homogeneous Decaying Turbulence
As the representative of the shock-capturing scheme, the Roe scheme fails to
LES because important turbulent characteristics cannot be reproduced such as
the famous k-5/3 spectral law owing to large numerical dissipation. In this
paper, the Roe scheme is divided into five parts: , , , , and , which means
basic upwind dissipation, pressure-difference-driven and
velocity-difference-driven modification of the interface fluxes and pressure,
respectively. Then, the role of each part on LES is investigated by homogeneous
decaying turbulence. The results show that the parts , , and have little effect
on LES. It is important especially for because it is necessary for computation
stability. The large numerical dissipation is due to and , and each of them has
much larger dissipation than SGS dissipation. According to these understanding,
an improved all-speed LES-Roe scheme is proposed, which can give enough good
LES results for even coarse grid resolution with usually adopted
reconstruction
On plurisubharmonicity of the solution of the Fefferman equation and its applications to estimate the bottom of the spectrum of Laplace-Beltrami operators
In this paper, we introduce a concept of super-pseudoconvex domain. We prove
that the solution of the Feffereman equation on a smoothly bounded strictly
pseudoconvex domain in \CC^n is plurisubharmonic if and only if is
super-pseudoconvex. As an application, we give a lower bound estimate the
bottom of the spectrum of Laplace-Beltrami operators when is
super-pseudoconvex by using the result of Li and Wang \cite{LiWang}
Quantum synchronization and quantum state sharing in irregular complex network
We investigate quantum synchronization phenomenon within the complex network
constituted by coupled optomechanical systems and prove the unknown identical
quantum states can be shared or distributed in the quantum network even though
the topology is varying. Considering a channel constructed by quantum
correlation, we show that quantum synchronization can sustain and maintain high
levels in Markovian dissipation for a long time. We analyze state sharing
process between two typical complex networks, that is, a small-world network
corresponding to linear motif state sharing and a scale-free network
corresponding to whole network sharing, respectively. Our results predict that
linked nodes can be directly synchronized in small-world network, but the whole
network will be synchronized only if some specific synchronization conditions
are satisfied. Furthermore, we give the synchronization conditions analytically
through analyzing network dynamics. This proposal paves the way for studying
multi-interaction synchronization and achieving an effective quantum
information processing in complex network
Criterion of quantum synchronization and controllable quantum synchronization based on an optomechanical system
We propose a quantitative criterion to determine whether the coupled quantum
systems can achieve complete synchronization or phase synchronization in the
process of analyzing quantum synchronization. Adopting the criterion, we
discuss the quantum synchronization effects between optomechanical systems and
find that the error between the systems and the fluctuation of error are
sensitive to coupling intensity by calculating the largest Lyapunov exponent of
the model and quantum fluctuation, respectively. Through taking the appropriate
coupling intensity, we can control quantum synchronization even under different
logical relationship between switches. Finally, we simulate the dynamical
evolution of the system to verify the quantum synchronization criterion and to
show the ability of synchronization control
The asymptotic value of graph energy for random graphs with degree-based weights
In this paper, we investigate the energy of a weighted random graph
in , in which each edge takes the weight , where
is a random variable, the degree of vertex in the random graph
of the Erd\"{o}s--R\'{e}nyi random graph model , and is a
symmetric real function on two variables. Suppose for
some constants , and . Then,
for almost all graphs in , the energy of is
where
is any fixed and independent of . Consequently, with this one basket we can
get the asymptotic values of various kinds of graph energies of chemical use,
such as Randi\'c energy, ABC energy, and energies of random matrices obtained
from various kinds of degree-based chemical indices.Comment: 13 page
Asymmetrical interaction induced real spectra and exceptional points in a non-Hermitian Hamiltonian
Non-Hermitian systems with parity-time symmetry have been developed rapidly
and hold great promise for future applications. Unlike most existing works
considering the symmetry of the free energy terms (e.g., gain-loss system), in
this paper, we report that a realizable non-Hermitian interaction between two
quantum resonances can also have a real spectrum after the exceptional point.
That phenomenon is similar with that in the gain-loss system so that the
non-Hermitian interaction can be an excellent substitute for quantum gain. Such
a non-Hermitian interaction can be realized in designed optomechanics, and we
find that its dynamics are in accordance with those of normal gain system as
expected. As examples, the phase transition near the exceptional point and the
induced chaos in weak nonlinear coupling are shown and analyzed for an
intuitive visual. Our results provide a platform for realizing parity-time
symmetry devices and studying properties of non-Hermitian quantum mechanics
Sparse Recovery with Coherent Tight Frames via Analysis Dantzig Selector and Analysis LASSO
This article considers recovery of signals that are sparse or approximately
sparse in terms of a (possibly) highly overcomplete and coherent tight frame
from undersampled data corrupted with additive noise. We show that the properly
constrained -analysis, called analysis Dantzig selector, stably recovers a
signal which is nearly sparse in terms of a tight frame provided that the
measurement matrix satisfies a restricted isometry property adapted to the
tight frame. As a special case, we consider the Gaussian noise. Further, under
a sparsity scenario, with high probability, the recovery error from noisy data
is within a log-like factor of the minimax risk over the class of vectors which
are at most sparse in terms of the tight frame. Similar results for the
analysis LASSO are showed.
The above two algorithms provide guarantees only for noise that is bounded or
bounded with high probability (for example, Gaussian noise). However, when the
underlying measurements are corrupted by sparse noise, these algorithms perform
suboptimally. We demonstrate robust methods for reconstructing signals that are
nearly sparse in terms of a tight frame in the presence of bounded noise
combined with sparse noise. The analysis in this paper is based on the
restricted isometry property adapted to a tight frame, which is a natural
extension to the standard restricted isometry property.Comment: 21 pages; Corrected some typos and grammatical error
Multi-fold Darboux transformations of the extended bigraded Toda hierarchy
With the extended logarithmic flow equations and some extended Vertex
operators in generalized Hirota bilinear equations, extended bigraded Toda
hierarchy(EBTH) was proved to govern the Gromov-Witten theory of orbiford
in literature. The generating function of these Gromov-Witten
invariants is one special solution of the EBTH. In this paper, the multi-fold
Darboux transformations and their determinant representations of the EBTH are
given with two different gauge transformation operators. The two Darboux
transformations in different directions are used to generate new solutions from
known solutions which include soliton solutions of -EBTH, i.e. the EBTH
when . From the generation of new solutions, one can find the big
difference between the EBTH and the extended Toda hierarchy(ETH). Meanwhile we
plotted the soliton graphs of the -EBTH from which some approximation
analysis will be given. From the analysis on velocities of soliton solutions,
the difference between the extended flows and other flows are shown. The two
different Darboux transformations constructed by us might be useful in
Gromov-Witten theory of orbiford .Comment: 26 pages, accepted by Zeitschrift f\"ur Naturforschung
Restricted -Isometry Properties Adapted to Frames for Nonconvex -Analysis
This paper discusses reconstruction of signals from few measurements in the
situation that signals are sparse or approximately sparse in terms of a general
frame via the -analysis optimization with . We first introduce
a notion of restricted -isometry property (-RIP) adapted to a dictionary,
which is a natural extension of the standard -RIP, and establish a
generalized -RIP condition for approximate reconstruction of signals via the
-analysis optimization. We then determine how many random, Gaussian
measurements are needed for the condition to hold with high probability. The
resulting sufficient condition is met by fewer measurements for smaller
than when .
The introduced generalized -RIP is also useful in compressed data
separation. In compressed data separation, one considers the problem of
reconstruction of signals' distinct subcomponents, which are (approximately)
sparse in morphologically different dictionaries, from few measurements. With
the notion of generalized -RIP, we show that under an usual assumption that
the dictionaries satisfy a mutual coherence condition, the split analysis
with can approximately reconstruct the distinct components from
fewer random Gaussian measurements with small than when Comment: 40 pages, 1 figure, under revision for a journa
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