Interaction energy between vortices of vector fields on Riemannian surfaces

We study a variational Ginzburg–Landau-type model depending on a small parameter $\epsilon >0$ for (tangent) vector fields on a 2-dimensional Riemannian surface. As $\epsilon \to 0$, the vector fields tend to be of unit length and will have singular points of a (non-zero) index, called vortices. Our main result determines the interaction energy between these vortices as a Γ-limit (at the second order) as $\epsilon \to 0$.     

Nonclassical rotational inertia of a supersolid

As proposed by Leggett [Phys. Rev. Lett. 25, 1543 (1970)10.1103/PhysRevLett.25.1543], the supersolidity of a crystal is characterized by the nonclassicalical Rotational Inertia (NCRI) property. Using a model of quantum crystal introduced by Josserand, Pomeau, and Rica [Phys. Rev. Lett. 72, 2426 (1994)10.1103/PhysRevLett.72.2426], we prove that NCRI occurs. This is done by analyzing the ground state of the aforementioned model, which is related to a sphere packing problem, and then deriving a theoretical formula for the moment of inertia. We infer a lower estimate for the NCRI fraction, which is a landmark of supersolidity.     

Extended Hückel calculations of the ionization potentials of some conjugated hydrocarbons

The prediction of ionization potentials of conjugated hydrocarbons using extended Hückel theory is reevaluated. Consequently, two major modifications to the theory are proposed and then tested on five sample molecules. Allowance for distinct sigma and pi orbital parameters as well as for diagonal and off-diagonal parameters constitute the changes examined and are shown to arise naturally from the theory. Subsequent testing of the reproduction of photoelectron spectra indicates significant improvements over previous usage of extended Hückel theory.