Related papers: Wave vector substar group in reciprocal lattice sp…
We construct a large class of examples of the cyclic sieving phenomenon by expoiting the representation theory of semi-simple Lie algebras. Let $M$ be a finite dimensional representation of a semi-simple Lie algebra and let $B$ be the…
How are the symmetries encoded in quasicrystals? As a compensation for the lack of translational symmetry, quasicrystals admit non-crystallographic symmetries such as 5- and 8-fold rotations in two-dimensional space. It is originated from…
We perform a three dimensional lattice simulation of the electroweak symmetry breaking process through a two-step phase transition, where one of the two steps is a first order phase transition. Our results show that: 1) when the electroweak…
We investigate the representations of the symmetry groups of infinite crystals. Crystal symmetries are usually described as the finite symmetry group of a finite crystal with periodic boundary conditions, for which the Brillouin zone is a…
Novel optical elements containing semitransparent wavelike films embedded into the bulk of transparent material, which form a reflection image without transmitted light distortion, are studied. The dynamic theory of light diffraction by a…
We describe here in detail the recently introduced methodology for simulation of structural transitions in crystals. The applications of the new scheme are illustrated on various kinds of crystals and the advantages with respect to previous…
We construct a crystal base of the negative half of a quantum orthosymplectic superalgebra. It can be viewed as a limit of the crystal bases of $q$-deformed irreducible oscillator representations. We also give a combinatorial description of…
A fundamental idea in wave mechanics is that propagation in a periodic medium can be described by Bloch waves whose conserved crystal momenta define their transformations when displaced by the set of discrete lattice translations. In…
Continuous symmetries and their breaking play a prominent role in contemporary physics. Effective low-energy field theories around symmetry breaking states explain diverse phenomena such as superconductivity, magnetism, and the mass of…
The analysis of Fourier-transformed scanning-tunneling-microscopy (STM) images with subatomic resolution is a common tool for studying properties of quasiparticle excitations in strongly correlated materials. While Fourier amplitudes are…
Symmetry of the crystal lattice can be a determining factor for the structure of Cooper pairs in unconventional superconductors. In this study we extend the discussion of superconductivity in non-centrosymmetric materials to the case when…
Superconductors exhibit unconventional electronic and magnetic properties if the Cooper pair wave function breaks additional symmetries of the normal phase. Rotational symmetries in spin- and orbital spaces, as well as discrete symmetries…
The discovery of quasicrystals has changed our view of some of the most basic notions related to the condensed state of matter. Before the age of quasicrystals, it was believed that crystals break the continuous translation and rotation…
When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two dimensional systems were predicted to spontaneously break continuous translation symmetry and form a quantum crystal. Efforts to observe this…
The wavelike processes of crystallisation and melting or crystallisation waves are well-known to exist at the crystal 4He surface in its rough state. Below the roughening transition temperature the crystal surface experiences the transition…
We study mean-field states resulting from the pairing of electrons in time-reversal broken fractal Hofstadter bands, which arise in two-dimensional lattices where the unit cell traps magnetic flux $\Phi = (p/q)\Phi_0$ comparable to the flux…
We present the results of a theoretical analysis of two-dimensionally modulated incommensurate phases in crystals and define the space distribution of magnetization and polarization vector in the incommensurate phase and demonstrate that…
Abstract Characterizing the crystalline disorder properties of the heterovalent ternary semiconductors continues to challenge solid-state theory. Here, a Landau theory is developed for the wurtzite-based ternary semiconductor ZnSnN2. It is…
We present a field theoretical model of point-form dynamics which exhibits resonance scattering. In particular, we construct point-form Poincar\'e generators explicitly from field operators and show that in the vector spaces for the…
We investigate lattices of instantons and the dimension-changing transitions between them. Our ultimate goal is the 3D->4D transition, which is holographically dual to the phase transition between the baryonic and the quarkyonic phases of…