660 research outputs found
Numerical Strategies of Computing the Luminosity Distance
We propose two efficient numerical methods of evaluating the luminosity
distance in the spatially flat {\Lambda}CDM universe. The first method is based
on the Carlson symmetric form of elliptic integrals, which is highly accurate
and can replace numerical quadratures. The second method, using a modified
version of Hermite interpolation, is less accurate but involves only basic
numerical operations and can be easily implemented. We compare our methods with
other numerical approximation schemes and explore their respective features and
limitations. Possible extensions of these methods to other cosmological models
are also discussed.Comment: 4 pages, 2 figures. v2: A minor error in the last equation has been
corrected (conclusions are not affected). v3: Accepted by MNRA
Analytical solutions to the spin-1 Bose-Einstein condensates
We analytically solve the one-dimensional coupled Gross-Pitaevskii equations
which govern the motion of F=1 spinor Bose-Einstein condensates. The nonlinear
density-density interactions are decoupled by making use of the unique
properties of the Jacobian elliptical functions. Several types of complex
stationary solutions are deduced. Furthermore, exact non-stationary solutions
to the time-dependent Gross-Pitaevskii equations are constructed by making use
of the spin-rotational symmetry of the Hamiltonian. The spin-polarizations
exhibit kinked configurations. Our method is applicable to other coupled
nonlinear systems.Comment: 12 figure
4,6-Dichloro-5-(2-methÂoxyÂphenÂoxy)-2,2′-bipyrimidine
In the title compound, C15H10Cl2N4O2, the dichloroÂpyrimidine and methÂoxyÂphenÂoxy parts are approximately perpendicular [dihedral angle = 89.9 (9)°]. The dihedral angle between the two pyrimidine rings is 36.3 (4)° In the crystal, there are no hydrogen bonds but the molÂecules are held together by short interÂmolecular C⋯N [3.206 (3) Å] contacts and C—H⋯π interÂactions
Maximum Relative Entropy of Coherence for Quantum Channels
Based on the resource theory for quantifying the coherence of quantum
channels, we introduce a new coherence quantifier for quantum channels via
maximum relative entropy. We prove that the maximum relative entropy for
coherence of quantum channels is directly related to the maximally coherent
channels under a particular class of superoperations, which results in an
operational interpretation of the maximum relative entropy for coherence of
quantum channels. We also introduce the conception of sub-superchannels and
sub-superchannel discrimination. For any quantum channels, we show that the
advantage of quantum channels in sub-superchannel discrimination can be exactly
characterized by the maximum relative entropy of coherence for quantum
channels. Similar to the maximum relative entropy of coherence for channels,
the robustness of coherence for quantum channels has also been investigated. We
show that the maximum relative entropy of coherence for channels provides new
operational interpretations of robustness of coherence for quantum channels and
illustrates the equivalence of the dephasing-covariant superchannels,
incoherent superchannels, and strictly incoherent superchannels in these two
operational tasks
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