This paper studies a class of Abelian varieties that are of $mathrm{GL}_2$-type and with isogenous classes defined over a number field $k$ (i.e., $k$-virtual). We treat both cases when their endomorphism algebras are (1) a totally real field $K$ or (
2) a totally indefinite quaternion algebra over a totally real field $K$. Among the isogenous class of such an Abelian variety, we identify one whose Galois conjugates can be described in terms of Atkin-Lehner operators and certain action of the class group of $K$. We deduce that such Abelian varieties are parametrised by finite quotients of certain PEL Shimura varieties. These new families of moduli spaces are further analysed when they are of dimension $2$. We provide explicit numerical bounds for when they are surfaces of general type. In addition, for two particular examples, we calculate precisely the coordinates of inequivalent elliptic points, study intersections of certain Hirzebruch cycles with exceptional divisors. We are able to show that they are both rational surfaces.
We investigated SrFe$mathrm{_2}$(As$mathrm{_{1-x}}$P$mathrm{_x}$)$mathrm{_2}$ single crystals with four different phosphorus concentrations x in the superconducting phase (x = 0.35, 0.46) and in the magnetic phase (x = 0, 0.2). The superconducting sa
mples display a V-shaped superconducting gap, which suggests nodal superconductivity. Furthermore we determined the superconducting coherence length by measuring the spatially resolved superconducting density of states (DOS). Using inelastic tunneling spectroscopy we investigated excitations in the samples with four different phosphorus concentrations. Inelastic peaks are related to bosonic modes. Phonon and non-phonon mechanism for the origin of these peaks are discussed.
We prove that functions of locally bounded deformation on $mathbb{R}^n$ are $mathrm{L}^{n/(n-1)}$-differentiable almost everywhere. More generally, we show that this critical $mathrm{L}^p$-differentiability result holds for functions of locally bound
ed $mathbb{A}$-variation, provided that the first order, homogeneous, linear differential operator $mathbb{A}$ has finite dimensional null-space.
A recent inelastic neutron scattering experiment on $mathrm{Yb}_2 mathrm{Ti}_2 mathrm{O}_7$ uncovers an unusual scattering continuum in the spin excitation spectrum despite the splayed ferromagnetic order in the ground state. While there exist well d
efined spin wave excitations at high magnetic fields, the one magnon modes and the two magnon continuum start to strongly overlap upon decreasing the field, and eventually they become the scattering continuum at zero field. Motivated by these observations, we investigate the possible emergence of a magnetically ordered ground state with fractionalized excitations in the spin model with the exchange parameters determined from two previous experiments. Using the fermionic parton mean field theory, we show that the magnetically ordered state with fractionalized excitations can arise as a stable mean field ground state in the presence of sufficiently strong quantum fluctuations. The spin excitation spectrum in such a ground state is computed and shown to have the scattering continuum. Upon increasing the magnetic field, the fractionalized magnetically ordered state is suppressed, and is eventually replaced by the conventional magnetically ordered phase at high fields, which is consistent with the experimental data. We discuss further implications of these results to the experiments and possible improvements on the theoretical analysis.
We present a precise measurement of double-polarization asymmetries in the $^3vec{mathrm{He}}(vec{mathrm{e}},mathrm{e}mathrm{d})$ reaction. This particular process is a uniquely sensitive probe of hadron dynamics in $^3mathrm{He}$ and the structure o
f the underlying electromagnetic currents. The measurements have been performed in and around quasi-elastic kinematics at $Q^2 = 0.25,(mathrm{GeV}/c)^2$ for missing momenta up to $270,mathrm{MeV}/c$. The asymmetries are in fair agreement with the state-of-the-art calculations in terms of their functional dependencies on $p_mathrm{m}$ and $omega$, but are systematically offset. Beyond the region of the quasi-elastic peak, the discrepancies become even more pronounced. Thus, our measurements have been able to reveal deficiencies in the most sophisticated calculations of the three-body nuclear system, and indicate that further refinement in the treatment of their two- and/or three-body dynamics is required.