High quality single crystals of BaFe$_{12}$O$_{19}$ were grown using the floating zone technique in flowing oxygen pressurized to 100 atm. Single crystal neutron diffraction was used to determine the nuclear and magnetic structure of BaFe$_{12}$O$_{19}$ at 4 K and 295 K. At both temperatures, there exist local electric dipoles formed by the off-mirror-plane displacements of magnetic Fe$^{3+}$ ions at the bipyramidal sites. The displacement at 4 K is about half of that at room temperature. The temperature dependence of the specific heat shows no anomaly associated with long range polar ordering in the temperature range from 1.90-300 K. The inverse dielectric permittivity, $1/varepsilon$, along the c-axis shows a $T^2$ temperature dependence between 10 K and 20 K, with a significantly reduced temperature dependence displayed below 10 K. Moreover, as the sample is cooled below 1.4 K there is an anomalous sharp upturn in $1/varepsilon$. These features resemble those of classic quantum paraelectrics such as SrTiO$_3$. The presence of the upturn in $1/varepsilon$ indicates that BaFe$_{12}$O$_{19}$ is a critical quantum paraelectric system with Fe$^{3+}$ ions involved in both magnetic and electric dipole formation.
This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This criterion uses the celebrated Huber function from the robust statistics literature to downweigh the effects of outliers. A practical algorithm is developed to solve the optimization involved. This algorithm is fast, straightforward to implement, and monotonic convergent. Furthermore, the proposed methodology is theoretically shown to be stable in a well defined sense. Its promising empirical performance is demonstrated via a sequence of simulation experiments, including image inpainting.
We show both theoretically and experimentally that a pair of inductively coupled active LRC circuits (dimer), one with amplification and another with an equivalent amount of attenuation, display all the features which characterize a wide class of non-Hermitian systems which commute with the joint parity-time PT operator: typical normal modes, temporal evolution, and scattering processes. Utilizing a Liouvilian formulation, we can define an underlying PT-symmetric Hamiltonian, which provides important insight for understanding the behavior of the system. When the PT-dimer is coupled to transmission lines, the resulting scattering signal reveals novel features which reflect the PT-symmetry of the scattering target. Specifically we show that the device can show two different behaviors simultaneously, an amplifier or an absorber, depending on the direction and phase relation of the interrogating waves. Having an exact theory, and due to its relative experimental simplicity, PT-symmetric electronics offers new insights into the properties of PT-symmetric systems which are at the forefront of the research in mathematical physics and related fields.
We investigate the low-field relaxation of nuclear hyperpolarization in undoped and highly doped silicon microparticles at room temperature following removal from high field. For nominally undoped particles, two relaxation time scales are identified for ambient fields above 0.2 mT. The slower, T_1s, is roughly independent of ambient field; the faster, T_1f, decreases with increasing ambient field. A model in which nuclear spin relaxation occurs at the particle surface via a two-electron mechanism is shown to be in good agreement with the experimental data, particularly the field-independence of T_1s. For boron-doped particles, a single relaxation time scale is observed. This suggests that for doped particles, mobile carriers and bulk ionized acceptor sites, rather than paramagnetic surface states, are the dominant relaxation mechanisms. Relaxation times for the undoped particles are not affected by tumbling in a liquid solution.
A subbundle of variable dimension inside the tangent bundle of a smooth manifold is called a smooth distribution if it is the pointwise span of a family of smooth vector fields. We prove that all such distributions are finitely generated, meaning that the family may be taken to be a finite collection. Further, we show that the space of smooth sections of such distributions need not be finitely generated as a module over the smooth functions. Our results are valid in greater generality, where the tangent bundle may be replaced by an arbitrary vector bundle.
In the standard slow-roll inflationary cosmology, quantum fluctuations in a single field, the inflaton, generate approximately Gaussian primordial density perturbations. At present, the bispectrum and trispectrum of the density perturbations have not been observed and the probability distribution for these perturbations is consistent with Gaussianity. However, Planck satellite data will bring a new level of precision to bear on this issue, and it is possible that evidence for non-Gaussian effects in the primordial distribution will be discovered. One possibility is that a trispectrum will be observed without evidence for a non-zero bispectrum. It is not difficult for this to occur in inflationary models where quantum fluctuations in a field other than the inflaton contribute to the density perturbations. A natural question to ask is whether such an observation would rule out the standard scenarios. We explore this issue and find that it is possible to construct single-field models in which inflaton-generated primordial density perturbations have an observable trispectrum, but a bispectrum that is too small to be observed by the Planck satellite. However, an awkward fine tuning seems to be unavoidable.
We report quantum Monte Carlo calculations of biexciton binding energies in ideal two-dimensional bilayer systems with isotropic electron and hole masses. We have also calculated exciton-exciton interaction potentials, and pair distribution functions for electrons and holes in bound biexcitons. Comparing our data with results obtained in a recent study using a model exciton-exciton potential [C. Schindler and R. Zimmermann, Phys. Rev. B textbf{78}, 045313 (2008)], we find a somewhat larger range of layer separations at which biexcitons are stable. We find that individual excitons retain their identity in bound biexcitons for large layer separations.
The electron spin g- and hyperfine tensors of the endohedral metallofullerene Sc@C82 are anisotropic. Using electron spin resonance (ESR) and density functional theory (DFT), we can relate their principal axes to the coordinate frame of the molecule, finding that the g-tensor is not axially symmetric. The Sc bond with the cage is partly covalent and partly ionic. Most of the electron spin density is distributed around the carbon cage, but 5% is associated with the scandium d_yz orbital, and this drives the observed anisotropy.
The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics present in the template, such as size and symmetry, are broken down into components associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude, circulation, etc.) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and is able to reproduce known physical scaling laws when processing a set of voriticity fields that evolve over time.
