Related papers: Helicity -- from Clifford to Graphene

Two notions of riffle shuffling on finite Coxeter groups are given: one using Solomon's descent algebra and another using random walk on chambers of hyperplane arrangements. These coincide for types $A$,$B$,$C$, $H_3$, and rank two groups.…

A range of twist angles between adjacent surfaces/volumes are intrinsic to natural graphite or artificially design in multi-layer graphene. In addition, stacking faults can be created by the application of mechanic, electric or magnetic…

We present two geometric interpretations for complex multivectors and determinants: a little known one in terms of square roots of volumes, and a new one which uses fractions of volumes and allows graphical representations. The fraction…

The low energy excitations of graphene can be described by a massless Dirac equation in two spacial dimensions. Curved graphene is proposed to be described by coupling the Dirac equation to the corresponding curved space. This covariant…

We investigate the tension between symplecticity and gauge covariance in classical Hamiltonian mechanics. The pursuit of manifest covariance over manifest symplecticity results in a unique geometric formulation. Firstly, covariant yet…

We examine the structure of the Clifford algebra associated with a Hermitian bilinear form and apply the result to a dynamical model of the relativistic point particle. The dynamics of the particle is described by a Dirac spinor with…

We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…

Complementary idempotent paravectors and their ordered compositions, are used to represent multivector basis elements of geometric Clifford algebra for 3D Euclidean space as the states of a geometric byte in a given frame of reference. Two…

We start from a new theory (discussed earlier) in which the arena for physics is not spacetime, but its straightforward extension-the so called Clifford space ($C$-space), a manifold of points, lines, areas, etc..; physical quantities are…

We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics…

For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning it must be invariant under two groups of…

This article reviews silicene, a relatively new allotrope of silicon, which can also be viewed as the silicon version of graphene. Graphene is a two-dimensional material with unique electronic properties qualitatively different from those…

We apply the semi-classical quantum Boltzmann formalism for the computation of transport properties to multilayer graphene. We compute the electrical conductivity as well as the thermal conductivity and thermopower for Bernal-stacked…

We study point particles in 2+1 dimensional first order gravity using a triangulation to fix the connection and frame-field. The Hamiltonian is reduced to a boundary term which yields the total mass. The triangulation is dynamical with…

At the tree level, the maximally helicity violating amplitudes of N gauge bosons in open superstring theory and of N gravitons in supergravity are known to have simple representations in terms of tree graphs. For superstrings, the graphs…

The barotropic ideal fluid with step and delta-function discontinuities coupled to Einstein's gravity is studied. The discontinuities represent star surfaces and thin shells; only non-intersecting discontinuity hypersurfaces are considered.…

This is a concise review of holographic superconductors and superfluids. We highlight some predictions of the holographic models and the emphasis is given to physical aspects rather than to the technical details, although some references to…

This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…

We develop Green's function formalism to describe continuous multi-layered quasi-one-dimensional setups described by piece-wise constant single-particle Hamiltonians. The Hamiltonians of the individual layers are assumed to be quadratic…

Graphene is a one-atom-thick sheet of carbon atoms arranged in a honeycomb lattice. It was first obtained by exfoliation of graphite in 2004 and has since evolved into a thriving research topic because of its attractive mechanical, thermal,…