11,876 research outputs found
On groups all of whose Haar graphs are Cayley graphs
A Cayley graph of a group is a finite simple graph such that
contains a subgroup isomorphic to acting regularly on
, while a Haar graph of is a finite simple bipartite graph
such that contains a subgroup isomorphic to
acting semiregularly on and the -orbits are equal to the
bipartite sets of . A Cayley graph is a Haar graph exactly when it is
bipartite, but no simple condition is known for a Haar graph to be a Cayley
graph. In this paper, we show that the groups and
are the only finite inner abelian groups all of whose Haar graphs are
Cayley graphs (a group is called inner abelian if it is non-abelian, but all of
its proper subgroups are abelian). As an application, it is also shown that
every non-solvable group has a Haar graph which is not a Cayley graph.Comment: 17 page
Arc-transitive cyclic and dihedral covers of pentavalent symmetric graphs of order twice a prime
A regular cover of a connected graph is called {\em cyclic} or {\em dihedral}
if its transformation group is cyclic or dihedral respectively, and {\em
arc-transitive} (or {\em symmetric}) if the fibre-preserving automorphism
subgroup acts arc-transitively on the regular cover. In this paper, we give a
classification of arc-transitive cyclic and dihedral covers of a connected
pentavalent symmetric graph of order twice a prime. All those covers are
explicitly constructed as Cayley graphs on some groups, and their full
automorphism groups are determined
On cubic symmetric non-Cayley graphs with solvable automorphism groups
It was proved in [Y.-Q. Feng, C. H. Li and J.-X. Zhou, Symmetric cubic graphs
with solvable automorphism groups, {\em European J. Combin.} {\bf 45} (2015),
1-11] that a cubic symmetric graph with a solvable automorphism group is either
a Cayley graph or a -regular graph of type , that is, a graph with no
automorphism of order interchanging two adjacent vertices. In this paper an
infinite family of non-Cayley cubic -regular graphs of type with a
solvable automorphism group is constructed. The smallest graph in this family
has order 6174.Comment: 8 page
Entanglement generation and manipulation in the Hong-Ou-Mandel experiment: A hidden scenario beyond two-photon interference
Hong-Ou-Mandel (HOM) effect was long believed to be a two-photon interference
phenomenon. It describes the fact that two indistinguishable photons mixed at a
beam splitter will bunch together to one of the two output modes. Considering
the two single-photon emitters such as trapped ions, we explore a hidden
scenario of the HOM effect, where entanglement can be generated between the two
ions when a single photon is detected by one of the detectors. A second photon
emitted by the entangled photon sources will be subsequently detected by the
same detector. However, we can also control the fate of the second photon by
manipulating the entangled state. Instead of two-photon interference, phase of
the entangled state is responsible for photon's path in our proposal. Toward a
feasible experimental realization, we conduct a quantum jump simulation on the
system to show its robustness against experimental errors.Comment: 16 pages, 5 figure
On basic graphs of symmetric graphs of valency five
A graph \G is {\em symmetric} or {\em arc-transitive} if its automorphism
group \Aut(\G) is transitive on the arc set of the graph, and \G is {\em
basic} if \Aut(\G) has no non-trivial normal subgroup such that the
quotient graph \G_N has the same valency with \G. In this paper, we
classify symmetric basic graphs of order and valency 5, where are
two primes and is a positive integer. It is shown that such a graph is
isomorphic to a family of Cayley graphs on dihedral groups of order with
5\di (q-1), the complete graph of order , the complete bipartite
graph of order 10, or one of the nine sporadic coset graphs
associated with non-abelian simple groups. As an application, connected
pentavalent symmetric graphs of order for some small integers and
are classified
TeV-PeV neutrinos over the atmospheric background: originating from two groups of sources?
In addition to the two ~1 PeV neutrinos, the IceCube Collaboration recently
reported a detection of 26 neutrino candidates at energies from 30 TeV to 250
TeV, implying a confidence level of 4.3\sigma over the atmospheric background.
We suggest that these TeV-PeV non-atmospheric neutrinos may originate from two
groups of sources, motivated by the non-detection of neutrinos in the energy
range 250 TeV- 1 PeV in current data. If intrinsic, the non-detection of 250
TeV-1 PeV neutrinos disfavors the single power-law spectrum model for the
TeV-PeV non-atmospheric neutrinos at a confidence level of ~ 2\sigma. We then
interpret the current neutrino data with a two-component spectrum model. One
has a flat spectrum with a cutoff at the energy ~ 250 TeV and the other has a
sharp peak at ~1 PeV. The former is likely via pp collision while the latter
may be generated by the photomeson interaction.Comment: 5 pages, 1 figur
Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
Tsallis- entanglement is a bipartite entanglement measure which is the
generalization of entanglement of formation for tending to 1. We first
expand the range of for the analytic formula of Tsallis-\emph{q}
entanglement. For \frac{5-\sqrt{13}}{2} \leq \emph{q} \leq
\frac{5+\sqrt{13}}{2}, we prove the monogamy relation in terms of the squared
Tsallis- entanglement for an arbitrary multi-qubit systems. It is shown that
the multipartite entanglement indicator based on squared Tsallis-
entanglement still works well even when the indicator based on the squared
concurrence loses its efficacy. We also show that the -th power of
Tsallis-\emph{q} entanglement satisfies the monogamy or polygamy inequalities
for any three-qubit state.Comment: This paper was submitted on 27th Marc
Polygamy relation for the R\'enyi- entanglement of assistance in multi-qubit systems
We prove a new polygamy relation of multi-party quantum entanglement in terms
of R\'{e}nyi- entanglement of assistance for . This class of
polygamy inequality reduces to the polygamy inequality based on entanglement of
assistance since R\'{e}nyi- entanglement is a generalization of
entanglement of formation. We further show that the polygamy inequality also
holds for the th power of R\'{e}nyi- entanglement of assistance.Comment: 6 pages, 7 figure
Accelerating Optical Absorption Spectra and Exciton Energy Computation for Nanosystems via Interpolative Separable Density Fitting
We present an efficient way to solve the Bethe-Salpeter equation (BSE), a
model for the computation of absorption spectra in molecules and solids that
includes electron-hole excitations. Standard approaches to construct and
diagonalize the Bethe-Salpeter Hamiltonian require at least \O(N_e^5)
operations, where is proportional to the number of electrons in the
system, limiting its application to small systems. Our approach is based on the
interpolative separable density fitting (ISDF) technique to construct low rank
approximations to the bare and screened exchange operators associated with the
BSE Hamiltonian. This approach reduces the complexity of the Hamiltonian
construction to \O(N_e^3) with a much smaller pre-constant. Here, we
implement the ISDF method for the BSE calculations within the Tamm-Dancoff
approximation (TDA) in the BerkeleyGW software package. We show that ISDF-based
BSE calculations in molecules and solids reproduce accurate exciton energies
and optical absorption spectra with significantly reduced computational cost.Comment: 16 pages, 5 figures, submitted to International Conference on
Computational Scienc
A linear calibration method on DNL error for energy spectrum
A calibration method aimed for the differential nonlinearity (DNL) error of
the Low Energy X-ray Instrument (LE) onboard the Hard X-ray Modulation
Telescope (HXMT) is presented, which is independent with electronic systems
used as testing platform and is only determined by the analog-to-digital
converter (ADC) itself. Exploring this method, ADCs that are used within the
flight model phase of HXMT-LE can be calibrated individually and independently
by a non-destructive and low-cost way, greatly alleviating the complexity of
the problem. As a result, the performance of the energy spectrum can be
significantly improved, further more, noise reduced and resolution enhanced
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