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Register a new userReconstruction of densities from Compton profiles with applying Jacobi polynomials
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The advent of synchrotron sources has led to an increasing availability of high resolution Compton Profiles J(pz) and a consequent renewed interest in the reconstruction of the corresponding full momentum densities rho(p). We present results of applying a new method in which the radial parts of rho(p) and the measured profiles are expressed in terms of Jacobi polynomials. The technique is demonstrated using model projections that correspond to Mg and Gd spectra. Reconstructed densities, being in very good agreement with model ones, are a very good performance of our new reconstruction algorithm.
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A method for computing electron momentum densities and Compton profiles from ab initio calculations is presented. Reciprocal space is divided into optimally-shaped tetrahedra for interpolation, and the linear tetrahedron method is used to obtain the momentum density and its projections such as Compton profiles. Results are presented and evaluated against experimental data for Be, Cu, Ni, Fe3Pt, and YBa2Cu4O8, demonstrating the accuracy of our method in a wide variety of crystal structures.
The two-dimensional momentum density of Be on the basal GMK plane, i.e. the line integral of the three-dimensional momentum density along the c-axis, is reconstructed via the Cormack method from both experimental and theoretical Compton profiles. It is shown that in the case of Be, despite the momentum density is highly anisotropic, merely two Compton profiles are sufficient to reproduce the main features of the momentum density. The analysis of the reconstructed densities is performed both in the extended and reduced zone schemes.
Let ${bf P}_k^{(alpha, beta)} (x)$ be an orthonormal Jacobi polynomial of degree $k.$ We will establish the following inequality begin{equation*} max_{x in [delta_{-1},delta_1]}sqrt{(x- delta_{-1})(delta_1-x)} (1-x)^{alpha}(1+x)^{beta} ({bf P}_{k}^{(alpha, beta)} (x))^2 < frac{3 sqrt{5}}{5}, end{equation*} where $delta_{-1}<delta_1$ are appropriate approximations to the extreme zeros of ${bf P}_k^{(alpha, beta)} (x) .$ As a corollary we confirm, even in a stronger form, T. Erd{e}lyi, A.P. Magnus and P. Nevai conjecture [Erd{e}lyi et al., Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal. 25 (1994), 602-614], by proving that begin{equation*} max_{x in [-1,1]}(1-x)^{alpha+{1/2}}(1+x)^{beta+{1/2}}({bf P}_k^{(alpha, beta)} (x))^2 < 3 alpha^{1/3} (1+ frac{alpha}{k})^{1/6}, end{equation*} in the region $k ge 6, alpha, beta ge frac{1+ sqrt{2}}{4}.$
Electronic transport is at the heart of many phenomena in condensed matter physics and material science. Magnetic imaging is a non-invasive tool for detecting electric current in materials and devices. A two-dimensional current density can be reconstructed from an image of a single component of the magnetic field produced by the current. In this work, we approach the reconstruction problem in the framework of Bayesian inference, i.e. we solve for the most likely current density given an image obtained by a magnetic probe. To enforce a sensible current density priors are used to associate a cost with unphysical features such as pixel-to-pixel oscillations or current outside the device boundary. Beyond previous work, our approach does not require analytically tractable priors and therefore creates flexibility to use priors that have not been explored in the context of current reconstruction. Here, we implement several such priors that have desirable properties. A challenging aspect of imposing a prior is choosing the optimal strength. We describe an empirical way to determine the appropriate strength of the prior. We test our approach on numerically generated examples. Our code is released in an open-source texttt{python} package called texttt{pysquid}.
Two-dimensional angular correlation of annihilation radiation (2D-ACAR) and Compton scattering are both powerful techniques to investigate the bulk electronic structure of crystalline solids through the momentum density of the electrons. Here we apply both methods to a single crystal of Pd to study the electron momentum density and the occupancy in the first Brillouin zone, and to point out the complementary nature of the two techniques. To retrieve the 2D spectra from 1D Compton profiles, a new direct inversion method (DIM) is implemented and benchmarked against the well-established Cormacks method. The comparison of experimental spectra with first principles density functional theory calculations of the electron momentum density and the two photon momentum density clearly reveals the importance of positron probing effects on the determination of the electronic structure. While the calculations are in good agreement with the experimental data, our results highlight some significant discrepancies.
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