On the possibility of using X-ray Compton scattering to study magnetoelectrical properties of crystals

This paper discusses the possibility of using Compton scattering – an inelastic X-ray scattering process that yields a projection of the electron momentum density – to probe magnetoelectrical properties. It is shown that an antisymmetric component of the momentum density is a unique fingerprint of such time- and parity-odd physics. It is argued that polar ferromagnets are ideal candidates to demonstrate this phenomenon and the first experimental results are shown, on a single-domain crystal of GaFeO3. The measured antisymmetric Compton profile is very small (≃ 10−5of the symmetric part) and of the same order of magnitude as the statistical errors. Relativistic first-principles simulations of the antisymmetric Compton profile are presented and it is shown that, while the effect is indeed predicted by theory, and scales with the size of the valence spin–orbit interaction, its magnitude is significantly overestimated. The paper outlines some important constraints on the properties of the antisymmetric Compton profile arising from the underlying crystallographic symmetry of the sample.

Engineering two-photon high-dimensional states through quantum interference

Many protocols in quantum science, for example, linear optical quantum computing, require access to large-scale entangled quantum states. Such systems can be realized through many-particle qubits, but this approach often suffers from scalability problems. An alternative strategy is to consider a lesser number of particles that exist in high-dimensional states. The spatial modes of light are one such candidate that provides access to high-dimensional quantum states, and thus they increase the storage and processing potential of quantum information systems. We demonstrate the controlled engineering of two-photon high-dimensional states entangled in their orbital angular momentum through Hong-Ou-Mandel interference. We prepare a large range of high-dimensional entangled states and implement precise quantum state filtering. We characterize the full quantum state before and after the filter, and are thus able to determine that only the antisymmetric component of the initial state remains. This work paves the way for high-dimensional processing and communication of multiphoton quantum states, for example, in teleportation beyond qubits.

Strain Broadening of X-Ray Diffraction Peaks

The line shape caused by lattice distortions in a crystal is reviewed. It is revealed that the broadening of a diffraction peak with indices hkl is related to the mean-square-strain perpendicular to the reflecting (hkl) lattice planes. The strain broadening of line profiles depends on the order of diffraction. The line profiles for a crystal in which the lattice distortions are caused by dislocations are described in detail in this chapter. It is revealed that the anisotropic strain field of dislocations yields a special dependence of peak broadening on indices of reflection. The stronger the screening of the strain fields of dislocations, the longer the tails in the diffraction profiles. For polarized dislocation walls, the diffraction peak is asymmetric, and the antisymmetric component of the profile is determined by the dislocation polarization. It is shown that the strains in nanoparticles resulted by the relaxation of their surfaces also lead to line broadening.

High Balanced Biorthogonal Multiwavelets with Symmetry

Balanced multiwavelet transform can process the vector-valued data sparsely while preserving a polynomial signal. Yang et al. (2006) constructed balanced multiwavelets from the existing nonbalanced ones. It will be proved, however, in this paper that if the nonbalanced multiwavelets have antisymmetric component, it is impossible for the balanced multiwavelets by the method mentioned above to have symmetry. In this paper, we give an algorithm for constructing a pair of biorthogonal symmetric refinable function vectors from any orthogonal refinable function vector, which has symmetric and antisymmetric components. Then, a general scheme is given for high balanced biorthogonal multiwavelets with symmetry from the constructed pair of biorthogonal refinable function vectors. Moreover, we discuss the approximation orders of the biorthogonal symmetric refinable function vectors. An example is given to illustrate our results.

Foci in ray pencils of general divergency

In generalized optical systems, that is, in systems which may contain thin refracting elements of asymmetric dioptric power, pencils of rays may exhibit phenomena that cannot occur in conventional optical systems. In conventional optical systems astigmatic pencils have two principal meridians that are necessarily orthogonal; in generalized systems the principal meridians can be at any angle. In fact in generalized systems a pencil may have only one principal meridian or even none at all. In contrast to the line foci in the conventional interval of Sturm line foci in generalized systems may be at any angle and there may be only one line focus or no line foci. A conventional cylindrical pencil has a single line focus at a finite distance but it can be regarded as having a second line focus at infinity. Only in generalized systems is a single line focus possible without a second at infinity or anywhere else. The purpose of this paper is to illustrate the types of pencils possible in generalized systems. Particular attention is paid to the effect of including an antisymmetric component in the divergency of the pencil.

Retrieval Properties of a Hopfield Model with Random Asymmetric Interactions

The process of pattern retrieval in a Hopfield model in which a random antisymmetric component is added to the otherwise symmetric synaptic matrix is studied by computer simulations. The introduction of the antisymmetric component is found to increase the fraction of random inputs that converge to the memory states. However, the size of the basin of attraction of a memory state does not show any significant change when asymmetry is introduced in the synaptic matrix. We show that this is due to the fact that the spurious fixed points, which are destabilized by the introduction of asymmetry, have very small basins of attraction. The convergence time to spurious fixed-point attractors increases faster than that for the memory states as the asymmetry parameter is increased. The possibility of convergence to spurious fixed points is greatly reduced if a suitable upper limit is set for the convergence time. This prescription works better if the synaptic matrix has an antisymmetric component.

Planar Finite Forced Dynamics of a Double Hinged Circular Arch: Theory and Experiments

The planar dynamics of an elastic circular arch undergoing large displacements under a sinusoidally varying, concentrated, vertical force at its tip is analyzed. First, a revision of theoretical models found in the literature and an analysis on different analytical approximations consistent with different simplifying assumptions is done; then, the analytical results are compared with those of an experimental steel model of a double hinged circular arch. The principal region of instability of the unimodal symmetric solution in which the nonlinear modal coupling excites the antisymmetric component is studied; moreover, inside this principal instability region, subregions of instability of any periodic solution are found and the corresponding increased complexity of the time laws is analyzed by using time series analysis tools.

Cortical interactions in texture processing: Scale and dynamics

We investigate the neural computations underlying pattern processing with stimuli based on textures balanced for spatial frequency content (and second-order correlations) but not for higher-order correlations (Julesz et al. 1978). Interchange between two such isodipole textures produces a robust human visual evoked potential (VEP). The difference in population activity driven by two isodipole textures is quantified by the antisymmetric component of the VEP. Statistical properties of the textures eliminate contributions from linear mechanisms to the antisymmetric VEP.The dependence of the antisymmetric VEP on check size and fourth-order correlation statistics is used to test nonlinear models for the underlying neural computations. Linear summation, followed by a simple nonlinearity (such as rectification, saturation, or threshold), is inconsistent with the data. More elaborate models, in which a second nonlinear stage combines the output of local nonlinear mechanisms, are consistent with the data, provided that an appropriate spatial scale is chosen for the second stage of processing. For checks 4 min or smaller, the deduced interaction length is 10–15 min. For checks larger than 4 min, the interaction length is proportional to check size.