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We investigate one-electron properties of one-dimensional self-similar structures called limit quasi-periodic lattices. The trace map of such a lattice is nonconservative in contrast to the quasi-periodic case, and we can determine the…
We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the…
Periodic configurations have dominated the design of phononic and elastic-acoustic metamaterial structures for the past decades. Unlike periodic crystals, quasicrystals lack translational symmetry but are unrestricted in rotational…
We describe our recent work on the lattice formulation of N=4 three-dimensional super-Yang-Mills. Our formulation was based on the Donaldson-Witten twist, but we have also been studying the formulation based on the Blau-Thompson twist by…
One possible way to obtain the quasicrystallographic structures is the projections of the higher dimensional lattices into 2D or 3D subspaces. In this work we introduce a general technique applicable to any higher dimensional lattice. We…
This paper describes how one can use four standing wave laser fields to realize a two dimensional optical quasicrystal with eight-fold symmetry, closely related to the well-known octagonal or Ammann-Beenker tiling quasicrystal. We describe…
During the last several years a non-perturbative formulation of exact chiral symmetry on the lattice has been developed. I shall outline the main ideas of these developments and discuss prospects for the future. The focus will be on the…
We study the non-perturbative corrections generated by exotic instantons in U(N) gauge theories in eight and four dimensions. As it was shown previously, the eight-dimensional prepotential can be resummed using a plethystic formula showing…
Layered franckeite is a natural superlattice composed of two alternating layers of different compositions, SnS$_2$- and PbS-like. This creates incommensurability between the two species along the planes of the layers, resulting in…
In the wake of intense research on metamaterials the two-dimensional analogue, known as metasurfaces, has attracted progressively increasing attention in recent years due to the ease of fabrication and smaller insertion losses, while…
A series of thin layers of alternating refractive index is known to make a good optical mirror over certain bands of frequency. Such a device - often termed the Bragg reflector - is usually introduced to students within the first years of…
We introduce the Weighted Planar Stochastic Porous Lattice (WPSPL), a geometrically disordered substrate generated by iteratively subdividing a unit square. At each step a block is selected with probability proportional to its area, divided…
The resolution of conventional optical lenses is limited by the wavelength. Materials with negative refractive index have been shown to enable the generation of an enhanced resolution image where both propagating and non-propagating waves…
For many years, quasicrystals were observed only as solid-state metallic alloys, yet current research is now actively exploring their formation in a variety of soft materials, including systems of macromolecules, nanoparticles and colloids.…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…
Two-dimensional (2D) crystals have renewed opportunities in design and assembly of artificial lattices without the constraints of epitaxy. However, the lack of thickness control in exfoliated van der Waals (vdW) layers prevents realization…
We construct an infinite series of simply transitive irreducible lattices in PGL_2(F_q((t))) \times PGL_2(F_q((t))) by means of a quaternion algebra over F_q(t). The lattices depend on an odd prime power q = p^r and a parameter \tau\ in…
We investigate, in the context of a real massless scalar field in $1+1$ dimensions, models of partially reflecting mirrors simulated by Dirac $\delta-\delta^{\prime}$ point interactions. In the literature, these models do not exhibit full…
We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties of the subgroup such as whether it is quasiconvex, normal, finite-index or torsion-free. We…