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Transformers have achieved remarkable success across natural language processing (NLP) and computer vision (CV). However, deep transformer models often suffer from an over-smoothing issue, in which token representations converge to similar…
In this Colloquium, we review recent progress in the effective description of strongly-correlated phases of matter with spontaneously broken translations, such as charge density waves or Wigner crystals. In real materials, disorder is…
Neutron scattering experiments have recently been performed in the superconducting state of UPt3 to determine the structure of the vortex lattice. The data show anomalous field dependence of the aspect ratio of the unit cell in the B phase.…
Weber-type parabolic beams have a transverse intensity profile, which is parabolically-shaped and can be flexibly controlled. On the other hand, this type of beams belongs to the family of the so-called nondiffracting beams and have…
We develop a point-scattering approach to the plane-wave optical transmission of subwavelength metal hole arrays. We present a real space description instead of the more conventional reciprocal space description; this naturally produces…
In this paper, we continue the development of a new combinatorial model for the irreducible characters of a complex semisimple Lie group. This model, which will be referred to as the alcove path model, can be viewed as a discrete…
Spontaneous breaking of translational symmetry---known as `density wave' order---is common in nature. However such states are strongly sensitive to impurities or other forms of frozen disorder leading to fascinating glassy phenomena. We…
We study the representations of the commutator subgroup of the braid group with n strands in the symmetric group of degree r. Motivated by some experimental results, we conjecture that for n>r, every such representation is trivial.
We propose a mathematical description of crystal structure: underlying translational periodicity together with the distinct atomic positions up to the symmetry operations in the unit cell. It is consistent with the international table of…
We investigate theoretically globally nonuniform configurations of quantized-flux vortices in clean superconductors trapped by an external force field that induces a nonuniform vortex density profile. Using an extensive series of numerical…
In theories of supersymmetry breaking, it is often the case that there is more than one metastable vacuum. First-order phase transitions among such metastable vacua may generate a stochastic background of gravitational waves, the…
Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the…
Carrying digital information in traditional copper wires is becoming a major issue in electronic circuits. Optical connections such as fiber optics offers unprecedented transfer capacity, but the mismatch between the optical wavelength and…
We consider the possibility that the primordial fluctuations (scalar and tensor) might have been standing waves at their moment of creation, whether or not they had a quantum origin. We lay down the general conditions for spatial…
Interacting many-particle systems can self-organize into a rich variety of crystalline structures. While symmetry provides a powerful framework for predicting whether transitions between crystal states are continuous or discontinuous,…
The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given…
We study isometric representations of the semigroup $\mathbb{Z}_+\backslash \{1\}$. Notion of an inverse representation is introduced and a complete description (up to unitary equivalence) of such representations is given. Also, we study a…
Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…
When two-dimensional electrons are subjected to a very strong magnetic field, they are believed to form a triangular Wigner crystal. We demonstrate that, in the entire crystal phase, this crystal is very well represented by a…
We introduce a variational manifold of simple tensor network states for the study of a family of constrained models that describe spin-1/2 systems as realized by Rydberg atom arrays. Our manifold permits analytical calculation via…