Any component of moduli of polarized hyperkähler manifolds is dense in its deformation space

Let M be a compact hyperkähler manifold, and W the coarse moduli of complex deformations of M. Every positive integer class v   in H²(M)$H^2(M)$ defines a divisor _Dv$D_v$ in W consisting of all algebraic manifolds polarized by v. We prove that every connected component of this divisor is dense in W.     

Generic points of quadrics and Chow groups

In this article we study the sufficient conditions for the k̅-defined element of the Chow group of a smooth variety to be k-rational (defined over k). For 0-cycles this question was addressed earlier. Our methods work for cycles of arbitrary dimension. We show that it is sufficient to check this property over the generic point of a quadric of sufficiently large dimension. Among the applications one should mention the uniform construction of fields with all known u-invariants.     

Weak Solutions of the Navier–Stokes Equations for Compressible Flows in a Half-Space with No-Slip Boundary Conditions

We consider the Navier–Stokes equations for the motion of compressible, viscous flows in a half-space ${\mathbb{R}^n_+,}$ n =  2,  3, with the no-slip boundary conditions. We prove the existence of a global weak solution when the initial data are close to a static equilibrium. The density of the weak solution is uniformly bounded and does not contain a vacuum, the velocity is Hölder continuous in (x, t) and the material acceleration is weakly differentiable. The weak solutions of this type were introduced by D. Hoff in Arch Ration Mech Anal 114(1):15–46, (1991), Commun Pure and Appl Math 55(11):1365–1407, (2002) for the initial-boundary value problem in ${\Omega = \mathbb{R}^n}$ and for the problem in ${\Omega = \mathbb{R}^n_+}$ with the Navier boundary conditions.     

Loss of polarization entanglement in a fiber-optic system with polarization mode dispersion in one optical path

We characterize theoretically and experimentally the degradation of polarization entanglement in a fiber-optic entanglement distribution system where one of the optical fibers is exposed to the effects of polarization mode dispersion (PMD). We show gradual reduction of entanglement with increasing PMD and find that the highest PMD tolerance is achieved when the bandwidth of the pump used to generate the entangled photons in a χ((3)) process is approximately half the bandwidth of the quantum channels.     

Kapitza-Dirac diffraction without standing waves: diffraction without a grating?

We discuss electron diffraction from two counterpropagating light waves with two different frequencies. We show that, even though these waves do not form a standing wave, electron diffraction similar to the conventional Kapitza-Dirac effect, i.e., scattering on a standing wave, is still possible. The nonlinear response of the electron to the laser fields creates a stationary diffraction grating from which the same electron scatters.     

Coherent control of rotational wave-packet dynamics via fractional revivals

We show (i) how the evolution of a wave packet created from an initial thermal ensemble can be controlled by manipulating interferences during the wave packet's fractional revivals and (ii) how the wave-packet evolution can be mapped onto the dynamics of a few-state system, where the number of states is determined by the amount of information one wants to track about the wave packet in the phase space. We illustrate our approach by (i) switching off and on field-free molecular axis alignment induced by a strong laser pulse and (ii) converting alignment into field-free orientation, starting with rotationally cold or hot systems.     

An integral representation of functions in gas-kinetic models

Motivated by the theory of kinetic models in gas dynamics, we obtain an integral representation of lower semicontinuous functions on \({{\mathbb{R}}^d,}\)\({d\geq1}\). We use the representation to study the problem of compactness of a family of the solutions of the discrete time BGK model for the compressible Euler equations. We determine sufficient conditions for strong compactness of moments of kinetic densities, in terms of the measures from their integral representations.     

Locally conformally Kähler manifolds admitting a holomorphic conformal flow

A manifold M is locally conformally Kähler (LCK) if it admits a Kähler covering ${\tilde{M}}$ with monodromy acting by holomorphic homotheties. Let M be an LCK manifold admitting a holomorphic conformal flow of diffeomorphisms, lifted to a non-isometric homothetic flow on ${\tilde{M}}$ . We show that M admits an automorphic potential, and the monodromy group of its conformal weight bundle is ${\mathbb{Z}}$ .