Related papers: Polarizing Anisotropic Heisenberg Groups
Astrophysical polarization measurements provide some of the strongest constraints on the photon sector of the non-minimal Standard-Model Extension. This paper reviews some recent results obtained by combining optical linear and circular…
We give a complete characterization of the locally compact groups that are non-elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting…
The static dipole polarizability of metastable states in the kaonic helium atoms is studied. We use the complex coordinate rotation method to properly account for the resonant nature of the states. Our calculations show that some of the…
We present a new algorithm to compute all the chiral polytopes that have a given group $G$ as full automorphism group. This algorithm uses a new set of generators that characterize the group, all of them except one being involutions. It…
We study collisional rethermalization in ultracold dipolar thermal gases, made intricate by their anisotropic differential cross sections. Theoretical methods are provided to derive the number of collisions per rethermalization, which for…
The possibility of integration of two important categories of optical components, i.e., circular polarizer and lens, into a thin plasmonic metasurface is examined. After exploring general theoretical formulation, optimal designs to realize…
The aim of this paper is to study the existence of an Alt-Caffarelli-Friedman monotonicity type formula in the Heisenberg group.
We present the compact group approach to analysis of the long-wavelength dielectric and optical characteristics of substances which can be modeled as macroscopically homogeneous and isotropic systems of hard dielectric particles embedded…
We develop JSJ decomposition theory of pro-p groups.
Scattering of anisotropic radiation by atoms, ions or molecules is sufficient to generate linear polarization observable in stars and planets atmospheres, circumstellar environments, and in particular in the Sun's atmosphere. This kind of…
Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…
The complete group classification of a generalization of the Heath model is carried out by connecting it to the heat equation with nonlinear source. Examples of invariant solutions are given under the terminal and the barrier option…
Let G=O(n+3) be an orthogonal group of rank one and H=O(n+2) an anisotropic subgroup. We unwind the period along H of a spherical Eisenstein series of G against a cuspform of H into an Euler product and evaluate the local factors at odd…
We classify the module categories over the double (possibly twisted) of a finite group.
I give an outline of recent applications of the renormalisation group to effective theories of nuclear forces, focussing on the use of a Wilsonian approach to analyse systems of two or three nonrelativistic particles.
We completely characterize the range of $L^p$-boundedness of certain multilinear Radon-like transforms involving vertical projections in the Heisenberg group.
We show that polar actions of cohomogeneity two on simple compact Lie groups of higher rank, endowed with a biinvariant Riemannian metric, are hyperpolar. Combining this with a recent result of the second-named author, we are able to prove…
Polar dielectrics are a promising platform for mid-infrared nanophotonics, allowing for nanoscale electromagnetic energy confinement in oscillations of the crystal lattice. We recently demonstrated that in nanoscopic polar systems a local…
We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.
The problem of group classification of one class of quasilinear equations of hyperbolic type with two independent variables has been solved completely.