A multiscale approach to liquid crystal nematics via statistical field theory

We propose an approach to a multiscale problem in the theory of thermotropic uniaxial nematics based on the method of statistical field theory. This approach enables us to relate the coefficients $A$, $B$, $C$, $L_1$ and $L_2$ of the Landau-de Gennes free energy for the isotropic-nematic phase transition to the parameters of a molecular model of uniaxial nematics, which we take to be a lattice gas model of nematogenic molecules interacting via a short-ranged potential. We obtain general constraints on the temperature and volume fraction of nematogens for the Landau-de Gennes theory to be stable against molecular orientation fluctuations at quartic order. In particular, for the case of a fully occupied lattice, we compute the values of the isotropic-nematic transition temperature and the order parameter discontinuity predicted by (i) a continuum approximation of the nearest-neighbor Lebwohl-Lasher model and (ii) a Lebwohl-Lasher-type model with a nematogenic interaction of finite range. We find that the predictions of (i) are in reasonably good agreement with known results of MC simulation.Comment: 12 pages, 2 figure

Van der Waals torque and force between anisotropic topological insulator slabs

We investigate the character of the van der Waals (vdW) torque and force between two coplanar and dielectrically anisotropic topological insulator (TI) slabs separated by a vacuum gap in the non-retardation regime, where the optic axes of the slabs are each perpendicular to the normal direction to the slab-gap interface and also generally differently oriented from each other. We find that in addition to the magnetoelectric coupling strength, the anisotropy can also influence the sign of the vdW force, viz., a repulsive vdW force can become attractive if the anistropy is increased sufficiently. In addition, the vdW force oscillates as a function of the angular difference between the optic axes of the TI slabs, being most repulsive/least attractive (least repulsive/most attractive) for angular differences that are integer (half-integer) multiples of $\pi$. Our third finding is that the vdW torque for TI slabs is generally weaker than that for ordinary dielectric slabs. Our work provides the first instance in which the vector potential appears in a calculation of the vdW interaction for which the limit is non-retarded or static.Comment: 10 pages, 4 figure

Heavy Quark Spin Symmetry Violating Hadronic Transitions of Higher Charmonia

In heavy quarkonia, hadronic transitions serve as an enlightened probe for the structure and help to establish the understanding of light quark coupling with a heavy degree of freedom. Moreover, in recent years, hadronic transitions revealed remarkable discoveries to identify the new conventional heavy quarkonia and extracting useful information about the so called "XYZ" exotic states. In this contribution, we present our predictions for heavy quark spin symmetry (HQSS) breaking hadronic transitions of higher $S$ and $D$ wave vector charmonia based on our recently proposed model (inspired by Nambu-Jona-Lasinio (NJL) model) to create light meson(s) in heavy quarkonium transitions. We also suggest spectroscopic quantum numbers $(^{2S+1}L_J)$ for several observed charmoniumlike states. Our analysis indicates that the $Y(4360)$ is most likely to be a $3D$ dominant state.Comment: Proceedings of the talk presented at "XVII International Conference on Hadron Spectroscopy and Structure (Hadron2017)", 25-29 September 2017, Salamanca, Spai