18,426 research outputs found
On Wilson's Theorem and Polignac Conjecture
We introduce Wilson's theorem and Clement's result and present a necessary
and sufficient condition for p and p+2k to be primes where k is a positive
integer. By using Simiov's Theorem, we derive an improved version of Clement's
result and characterizations of Polignac twin primes which parallel previous
characterizations.Comment: 8 page
Nonaxisymmetric Rossby Vortex Instability with Toroidal Magnetic Fields in Radially Structured Disks
We investigate the global nonaxisymmetric Rossby vortex instability in a
differentially rotating, compressible magnetized accretion disk with radial
density structures. Equilibrium magnetic fields are assumed to have only the
toroidal component. Using linear theory analysis, we show that the density
structure can be unstable to nonaxisymmetric modes. We find that, for the
magnetic field profiles we have studied, magnetic fields always provide a
stabilizing effect to the unstable Rossby vortex instability modes. We discuss
the physical mechanism of this stabilizing effect. The threshold and properties
of the unstable modes are also discussed in detail. In addition, we present
linear stability results for the global magnetorotational instability when the
disk is compressible.Comment: ApJ accepte
State of the Art and Prospects of Structured Sensing Matrices in Compressed Sensing
Compressed sensing (CS) enables people to acquire the compressed measurements
directly and recover sparse or compressible signals faithfully even when the
sampling rate is much lower than the Nyquist rate. However, the pure random
sensing matrices usually require huge memory for storage and high computational
cost for signal reconstruction. Many structured sensing matrices have been
proposed recently to simplify the sensing scheme and the hardware
implementation in practice. Based on the restricted isometry property and
coherence, couples of existing structured sensing matrices are reviewed in this
paper, which have special structures, high recovery performance, and many
advantages such as the simple construction, fast calculation and easy hardware
implementation. The number of measurements and the universality of different
structure matrices are compared
Evolving nature of human contact networks with its impact on epidemic processes
Human contact networks are constituted by a multitude of individuals and
pairwise contacts among them. However, the dynamic nature, which generates the
evolution of human contact networks, of contact patterns is not known yet.
Here, we analyse three empirical datasets and identify two crucial mechanisms
of the evolution of temporal human contact networks, i.e. the activity state
transition laws for an individual to be socially active, and the contact
establishment mechanism that active individuals adopt. We consider both of the
two mechanisms to propose a temporal network model, named the memory driven
(MD) model, of human contact networks. Then we study the susceptible-infected
(SI) spreading processes on empirical human contact networks and four
corresponding temporal network models, and compare the full prevalence time of
SI processes with various infection rates on the networks. The full prevalence
time of SI processes in the MD model is the same as that in real-world human
contact networks. Moreover, we find that the individual activity state
transition promotes the spreading process, while, the contact establishment of
active individuals suppress the prevalence. Apart from this, we observe that
even a small percentage of individuals to explore new social ties is able to
induce an explosive spreading on networks. The proposed temporal network
framework could help the further study of dynamic processes in temporal human
contact networks, and offer new insights to predict and control the diffusion
processes on networks
Reformulating the Quantum Uncertainty Relation
Uncertainty principle is one of the cornerstones of quantum theory. In the
literature, there are two types of uncertainty relations, the operator form
concerning the variances of physical observables and the entropy form related
to entropic quantities. Both these forms are inequalities involving pairwise
observables, and are found to be nontrivial to incorporate multiple
observables. In this work we introduce a new form of uncertainty relation which
may give out complete trade-off relations for variances of observables in pure
and mixed quantum systems. Unlike the prevailing uncertainty relations, which
are either quantum state dependent or not directly measurable, our bounds for
variances of observables are quantum state independent and immune from the
"triviality" problem of having zero expectation values. Furthermore, the new
uncertainty relation may provide a geometric explanation for the reason why
there are limitations on the simultaneous determination of different
observables in -dimensional Hilbert space.Comment: 15 pages, 2 figures; published in Scientific Report
A Necessary and Sufficient Criterion for the Separability of Quantum State
Quantum entanglement has been regarded as one of the key physical resources
in quantum information sciences. However, the determination of whether a mixed
state is entangled or not is generally a hard issue, even for the bipartite
system. In this work we propose an operational necessary and sufficient
criterion for the separability of an arbitrary bipartite mixed state, by virtue
of the multiplicative Horn's problem. The work follows the work initiated by
Horodecki {\it et. al.} and uses the Bloch vector representation introduced to
the separability problem by J. De Vicente. In our criterion, a complete and
finite set of inequalities to determine the separability of compound system is
obtained, which may be viewed as trade-off relations between the quantumness of
subsystems. We apply the obtained result to explicit examples, e.g. the
separable decomposition of arbitrary dimension Werner state and isotropic
state.Comment: 33 pages; published in Scientific Report
Equivalence theorem of uncertainty relations
We present an equivalence theorem to unify the two classes of uncertainty
relations, i.e., the variance-based ones and the entropic forms, which shows
that the entropy of an operator in a quantum system can be built from the
variances of a set of commutative operators. That means an uncertainty relation
in the language of entropy may be mapped onto a variance-based one, and vice
versa. Employing the equivalence theorem, alternative formulations of entropic
uncertainty relations stronger than existing ones in the literature are
obtained for qubit system, and variance based uncertainty relations for spin
systems are reached from the corresponding entropic uncertainty relations.Comment: 18 pages, 1 figure; published in J. Phys. A: Math. Theo
Quantum Entanglement of Neutrino Pairs
It is practically shown that a pair of neutrinos from tau decay can form a
flavor entangled state. With this kind of state we show that the locality
constrains imposed by Bell inequality are violated by the quantum mechanics,
and an experimental test of this effect is feasible within the earth's length
scale. Theoretically, the quantum entanglement of neutrino pairs can be
employed to the use of long distance cryptography distribution in a protocol
similar to the BB84.Comment: 7 pages, 5 eps figures; This paper has been withdrawn by the author
due to the efficiency of detection
Generation of Einstein-Podolsky-Rosen State via Earth's Gravitational Field
Although various physical systems have been explored to produce entangled
states involving electromagnetic, strong, and weak interactions, the gravity
has not yet been touched in practical entanglement generation. Here, we propose
an experimentally feasible scheme for generating spin entangled neutron pairs
via the Earth's gravitational field, whose productivity can be one pair in
every few seconds with the current technology. The scheme is realized by
passing two neutrons through a specific rectangular cavity, where the gravity
adjusts the neutrons into entangled state. This provides a simple and practical
way for the implementation of the test of quantum nonlocality and statistics in
gravitational field.Comment: 12 pages, 9 figure
Separable Decompositions of Bipartite Mixed States
We present a practical scheme for the decomposition of a bipartite mixed
state into a sum of direct products of local density matrices, using the
technique developed in Li and Qiao (Sci. Rep. 8: 1442, 2018). In the scheme,
the correlation matrix which characterizes the bipartite entanglement is first
decomposed into two matrices composed of the Bloch vectors of local states.
Then we show that the symmetries of Bloch vectors are consistent with that of
the correlation matrix, and the magnitudes of the local Bloch vectors are lower
bounded by the correlation matrix. Concrete examples for the separable
decompositions of bipartite mixed states are presented for illustration.Comment: 22 pages; published in Quantum Inf. Proces
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