Infinite bubbling in non-Kählerian geometry

In a holomorphic family \({(X_b)_{b\in B}}\) of non-Kählerian compact manifolds, the holomorphic curves representing a fixed 2-homology class do not form a proper family in general. The deep source of this fundamental difficulty in non-Kähler geometry is the explosion of the area phenomenon: the area of a curve \({C_b\subset X_b}\) in a fixed 2-homology class can diverge as b → b ₀. This phenomenon occurs frequently in the deformation theory of class VII surfaces. For instance it is well known that any minimal GSS surface X ₀ is a degeneration of a 1-parameter family of simply blown up primary Hopf surfaces \({(X_z)_{z\in D{\setminus}\{0\}}}\) , so one obtains non-proper families of exceptional divisors \({E_z\subset X_z}\) whose area diverge as z → 0. Our main goal is to study in detail this non-properness phenomenon in the case of class VII surfaces. We will prove that, under certain technical assumptions, a lift \({\widetilde E_z}\) of E _z in the universal cover \({\widetilde X_z}\) does converge to an effective divisor \({\widetilde E_0}\) in \({\widetilde X_0}\) , but this limit divisor is not compact. We prove that this limit divisor is always bounded towards the pseudo-convex end of \({\widetilde X_0}\) and that, when X ₀ is a minimal surface with global spherical shell, it is given by an infinite series of compact rational curves, whose coefficients can be computed explicitly. This phenomenon—degeneration of a family of compact curves to an infinite union of compact curves—should be called infinite bubbling. We believe that such a decomposition result holds for any family of class VII surfaces whose generic fiber is a blown up primary Hopf surface. This statement would have important consequences for the classification of class VII surfaces.     

On the Hausdorff volume in sub-Riemannian geometry

For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous function. We then prove that up to dimension 4 it is smooth, while starting from dimension 5, in corank 1 case, it is ${\mathcal {C}^{3}}$ (and ${\mathcal {C}^{4}}$ on every smooth curve) but in general not ${\mathcal {C}^{5}}$ . These results answer to a question addressed by Montgomery about the relation between two intrinsic volumes that can be defined in a sub-Riemannian manifold, namely the Popp and the Hausdorff volume. If the nilpotent approximation depends on the point (that may happen starting from dimension 5), then they are not proportional, in general.     

Limiting behavior for arrays of rowwise ρ *-mixing random variables

We study the limiting behavior of maximal partial sums for arrays of rowwise ?? ^*-mixing random variables and obtain some new results that improve the corresponding theorem of Zhu [M.H. Zhu, Strong laws of large numbers for arrays of rowwise ?? ^*-mixing random variables, Discrete Dyn. Nat. Soc., 2007, Article ID 74296, 6 pp., 2007].     

Some properties of the vertical structure operators for hydrostatic atmospheric models

Hydrostatic atmospheric models in a generalized vertical coordinate are considered. The governing equations are linearized with respect to a general basic state including arbitrary vertical variation of the reference temperature profile. Vertical structure equations are derived and studied for both continuous and discretized models. Some properties of vertical normal modes are defined and a comparison between continuous and discrete cases is made.     

Precosheaves of pro-sets and abelian pro-groups are smooth

Let D be the category of pro-sets (or abelian pro-groups). It is proved that for any Grothendieck site X, there exists a reflector from the category of precosheaves on X with values in D to the full subcategory of cosheaves. In the case of precosheaves on topological spaces, it is proved that any precosheaf is smooth, i.e. is locally isomorphic to a cosheaf. Constant cosheaves are constructed, and there are established connections with shape theory.     

Towards a Resolution of Dilemma: Nonlocality or Nonobjectivity?

This paper discusses a possible resolution of the nonobjectivity-nonlocality dilemma in quantum mechanics in the light of experimental tests of the Bell inequality for two entangled photons and a Bell-like inequality for a single neutron. My conclusion is that these experiments show that quantum mechanics is nonobjective: that is, the values of physical observables cannot be assigned to a system before measurement. Bell’s assumption of nonlocality has to be rejected as having no direct experimental confirmation, at least thus far. I also consider the relationships between nonobjectivity and contextuality. Specifically, I analyze the impact of the Kochen-Specker theorem on the problem of contextuality of quantum observables. I argue that, just as von Neumann’s “no-go” theorem, the Kochen-Specker theorem is based on assumptions that do not correspond to the real physical situation. Finally, I present a theory of measurement based on a classical, purely wave model (pre-quantum classical statistical field theory), a model that reproduces quantum probabilities. In this model continuous fields are transformed into discrete clicks of detectors. While this model is classical, it is nonobjective. In this case, nonobjectivity is the result of the dependence of experimental outcomes on the context of measurement, in accordance with Bohr’s view.     

J/ψ polarization in pp collisions at √s=7 TeV

The ALICE Collaboration has studied J/ψ production in pp collisions at √s=7 TeV at the LHC through its muon pair decay. The polar and azimuthal angle distributions of the decay muons were measured, and results on the J/ψ polarization parameters λ(θ) and λ(φ) were obtained. The study was performed in the kinematic region 2.5相似文献   

Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond

The zero-phonon transition rate of a nitrogen-vacancy center is enhanced by a factor of ～70 by coupling to a photonic crystal resonator fabricated in monocrystalline diamond using standard semiconductor fabrication techniques. Photon correlation measurements on the spectrally filtered zero-phonon line show antibunching, a signature that the collected photoluminescence is emitted primarily by a single nitrogen-vacancy center. The linewidth of the coupled nitrogen-vacancy center and the spectral diffusion are characterized using high-resolution photoluminescence and photoluminescence excitation spectroscopy.     

Ultrafast three-dimensional submicrometer-resolution readout of coherent optical-phonon oscillations with shaped unamplified laser pulses at 20 MHz

An ultrafast three-dimensional readout of coherent optical-phonon oscillations from a diamond film is demonstrated using temporally and spectrally shaped ultrashort laser pulses, delivered by a compact, oscillator-only laser system. This system integrates a long-cavity ytterbium-fiber-laser-pumped 30?fs Cr:forsterite oscillator with a photonic-crystal-fiber soliton frequency shifter and a periodically poled lithium niobate spectrum compressor, providing coherent Raman excitation and time-delayed interrogation of optical phonons in diamond at a 20?MHz repetition rate with a submicrometer spatial resolution.