相关论文: Quasicrystal model sets from overlapping self-simi…
Optical reflectivity as a simple diagnostic method for testing structural quality of icosahedral quasicrystals 2 The optical reflectivity of Al-based and Ti-based quasicrystalline and approximant samples were investigated versus the quality…
We study the quasisymmetric geometry of the Julia sets of McMullen maps $f_\lambda(z)=z^m+\lambda/z^\ell$, where $\ell$, $m\geq 2$ are integers satisfying $1/\ell+1/m<1$ and $\lambda\in\mathbb{C}\setminus\{0\}$. If the free critical points…
We introduce a relax-and-round approach embedding the quantum approximate optimization algorithm (QAOA) with $p\geq 1$ layers. We show for many problems, including Sherrington-Kirkpatrick spin glasses, that at $p=1$, it is as accurate as…
In a previous paper, the authors studied the radical filtration of a Weyl module $\Delta_\zeta(\lambda)$ for quantum enveloping algebras $U_\zeta(\overset\circ{\mathfrak g})$ associated to a finite dimensional complex semisimple Lie algebra…
In this paper, we construct a one-dimensional photonic quasicrystal by combining two incommensurate spatial harmonics, where the ratio of their periods is the irrational number \beta. We evaluate the photonic quasicrystal accurately by a…
We devise an ideal 3-dimensional octagonal quasicrystal that is based upon the 2-dimensional Ammann-Beenker tiling and that is potentially suitable for realization with patchy particles. Based on an analysis of its local environments we…
Self-assembly is the process in which the components of a system, whether molecules, polymers, or macroscopic particles, are organized into ordered structures as a result of local interactions between the components themselves, without…
We argue that the Quadratic Spinor Lagrangian approach allows us to approach the problem of forming a geometrical condensate of spinorial tetrads in a natural manner. This, along with considerations involving the discrete symmetries of…
We study how the singular behaviour of classical systems at bifurcations is reflected by their quantum counterpart. The semiclassical contributions of individual periodic orbits to trace formulae of Gutzwiller type are known to diverge when…
Q-groupoids and Q-algebroids are, respectively, supergroupoids and superalgebroids that are equipped with compatible homological vector fields. These new objects are closely related to the double structures of Mackenzie; in particular, we…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
In quantum information theory and statistical physics, symmetries of multiple copies, or replicas, of a system play a pivotal role. For unitary ensembles, these symmetries are encoded in the replicated commutant: the algebra of operators…
By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two-and four-component spinor wave functions, and Slater spinor orbitals…
We construct a quasiregular mapping in $\mathbb{R}^3$ that is the first to illustrate several important dynamical properties: the quasi-Fatou set contains wandering components; these quasi-Fatou components are bounded and hollow; and the…
We study percolation problems of overlapping objects where the underlying geometry is such that in D-dimensions, a subset of the directions has a lattice structure, while the remaining directions have a continuum structure. The resulting…
We consider the iteration of quasiregular maps of transcendental type from $\mathbb{R}^d$ to $\mathbb{R}^d$. In particular we study quasi-Fatou components, which are defined as the connected components of the complement of the Julia set.…
We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as…
Fractals and quasiperiodic structures share self-similarity as a structural property. Motivated by the link between Fibonacci fractals and quasicrystals which are scaled by the golden mean ratio $\frac{1+\sqrt{5}}{2}$, we introduce and…
In many condensed-matter systems, it is very useful to introduce a quasi-particle approach, which is based on some sort of linearization around a suitable background state. In order to be a systematic and controlled approximation, this…
Quasicrystals are characterized by quasi-periodic arrangements of atoms. The description of their mechanics involves deformation and a (so called phason) vector field accounting at macroscopic scale of local phase changes, due to atomic…