Weirdest Martensite: Smectic Liquid Crystal Microstructure And Weyl-poincaré Invariance

Smectic liquid crystals are remarkable, beautiful examples of materials microstructure, with ordered patterns of geometrically perfect ellipses and hyperbolas. The solution of the complex problem of filling three-dimensional space with domains of focal conics under constraining boundary conditions yields a set of strict rules, which are similar to the compatibility conditions in a martensitic crystal. Here we present the rules giving compatible conditions for the concentric circle domains found at two-dimensional smectic interfaces with planar boundary conditions. Using configurations generated by numerical simulations, we develop a clustering algorithm to decompose the planar boundaries into domains. The interfaces between different domains agree well with the smectic compatibility conditions. We also discuss generalizations of our approach to describe the full three-dimensional smectic domains, where the variant symmetry group is the Weyl-Poincaré group of Lorentz boosts, translations, rotations, and dilatations. © 2016 American Physical Society.1161

Quantum tomography for Dirac spinors

We present a tomographic scheme, based on spacetime symmetries, for the reconstruction of the internal degrees of freedom of a Dirac spinor. We discuss the circumstances under which the tomographic group can be taken as SU(2), and how this crucially depends on the choice of the gamma matrix representation. A tomographic reconstruction process based on discrete rotations is considered, as well as a continuous alternative.Comment: 9 pages, LaTeX; v2: minor changes, references added. A slightly revised version has been accepted for publication in Phys. Lett.

Information-theoretic Approach To Kinetic-energy Functionals: The Nearly Uniform Electron Gas

We strengthen the connection between information theory and quantum mechanical systems using a recently developed dequantization procedure which results in a decomposition of the kinetic energy as the sum of a classical term and a purely quantum term. For the nearly uniform electron gas, we thereby approximate the noninteracting kinetic energy as the sum of the Thomas-Fermi term, which is exact for the uniform electron gas, and the Weizsäcker term, which is proportional to the Fisher information. Electron correlation is included via a nonlocal analytical expression which is a functional of the (N-1)-conditional probability density. This expression is evaluated via a statistically rigorous Monte-Carlo procedure to obtain the correlation energy as a functional of the electron density. We show that this functional is well aproximated by a term which is proportional to the Shannon entropy. Thus the kinetic energy is expressed as the standard Thomas-Fermi term plus terms which are proportional to two of the cornerstones of information theory: the Fisher information, which is a measure of localization, and the Shannon entropy, which is a measure of delocalization. © 2010 Springer Science+Business Media, LLC.4817882Vedral, V., (2006) Introduction to Quantum Information Science, , Oxford: Oxford University PressFisher, R.A., (1925) Proc. Camb. Philos. Soc., 22, pp. 700-725Nagy, A., (2003) J. Chem. Phys., 119, pp. 9401-9405Romera, E., Dehesa, J.S., (2004) J. Chem. Phys., 120, pp. 8906-8912Sen, K.D., Antolín, J., Angulo, J.C., (2007) Phys. Rev. A, 76, p. 032502. , (7 pages)Parr, R.G., Yang, W., (1989) Density Functional Theory of Atoms and Molecules, , Oxford: Oxford University PressThomas, L.H., (1927) Proc. Cambridge Philos. Soc., 23, pp. 542-548Fermi, E., (1927) Rend. Accad. Lincei, 6, pp. 602-607von Weizsäcker, C.F., (1935) Z. Phys., 96, pp. 431-458Mosna, R.A., Hamilton, I.P., Delle Site, L., (2005) J. Phys. A, 38, pp. 3869-3878Mosna, R.A., Hamilton, I.P., Delle Site, L., (2006) J. Phys. A, 39, pp. L229-L235Hamilton, I.P., Mosna, R.A., Delle Site, L., (2007) Theor. Chem. Acct., 118, pp. 407-415Delle Site, L., (2007) J. Phys. A, 40, pp. 2787-2792Ghiringhelli, L.M., Delle Site, L., (2008) Phys. Rev. B, 77, p. 073104. , (4 pages