Related papers: A rigged configuration model for $B(\infty)$
A typical crystal is a finite piece of a material which may be invariant under some point symmetry group. If it is a so-called intrinsic higher-order topological insulator or superconductor, then it displays boundary modes at hinges or…
We give a method to produce representations of the braid group $B_n$ of $n-1$ generators ($n\leq \infty$). Moreover, we give sufficient conditions over a non unitary representation for being of this type. This method produces examples of…
The polyhedral realizations for crystal bases of the integrable highest weight modules of $U_q(\mathfrak{g})$ have been introduced in ([T.Nakashima, J. Algebra, vol.219, no. 2, (1999)]), which describe the crystal bases as sets of lattice…
The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture.…
We consider the simulation of non-abelian gauge potentials in ultracold atom systems with atom-field interaction in the $\Lambda$ configuration where two internal states of an atom are coupled to a third common one with a detuning. We find…
The conjecture that M-theory has the rank eleven Kac-Moody symmetry e11 implies that Type IIA and Type IIB string theories in ten dimensions possess certain infinite dimensional perturbative symmetry algebras that we determine. This…
We investigate a modified version of the $AB$ random sequential adsorption model. Specifically, this model involves the deposition of two distinct types of particles onto a lattice, with the constraint that different types cannot occupy…
Collapse modes in compressed simple cubic (SC) and body-centered cubic (BCC) periodic arrangements of elastic frictionless beads were studied numerically using the discrete element method. Under pure hydrostatic compression, the SC…
We consider invariant symplectic connections $\nabla$ on homogeneous symplectic manifolds $(M,\omega)$ with curvature of Ricci type. Such connections are solutions of a variational problem studied by Bourgeois and Cahen, and provide an…
We develop a theory of bicrystalline ideals, synthesizing Gr\"obner basis techniques and Kashiwara's crystal theory. This provides a unified algebraic, combinatorial, and computational approach that applies to ideals of interest, old and…
We show that the number of distinct topological states associated to a given knotted defect, $L$, in a nematic liquid crystal is equal to the determinant of the link $L$. We give an interpretation of these states, demonstrate how they may…
For a Kac-Moody algebra $\mathfrak{g}$ of rank $2$ and a fundamental weight $\lambda$, we explicitly give an isomorphism between the set of Lakshmibai-Seshadri paths $\mathbb{B}(\lambda)$ and monomial realization $\mathcal{M}(\lambda)$. As…
We show coordinate rings of open Richardson varieties are upper cluster algebras for any symmetrizable Kac--Moody type. We further show the coordinate rings of (generalized) open Richardson varieties on the twisted product of flag varieties…
The symmetries of critical ground states of two-dimensional lattice models are investigated. We show how mapping a critical ground state to a model of a rough interface can be used to identify the chiral symmetry algebra of the conformal…
Second-order Moller-Plesset perturbation theory (MP2) for ab initio simulations of solids is often limited by divergence or over-correlation issues, particularly in metallic, narrow-gap, and dispersion-stabilized systems. We develop and…
In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…
In the present work we have proposed the method that allows one to easily estimate hardness and bulk modulus of known or hypothetical solid phases from the data on Gibbs energy of atomization of the elements and corresponding covalent…
Computational methods for designing interactions between colloidal particles that induce self-assembly have received much attention for their promise to discover tailored materials. However, it often remains a challenge to translate…
In this article, we demonstrate a method for inducing reversible crystal-to-crystal transitions in binary mixtures of soft colloidal particles. Through a controlled decrease of salinity and increasingly dominating electrostatic…
Holographic superconductor model represents various inhomogeneous solutions with homogeneous sources. In this paper, we study inhomogeneous structures in the presence of the homogeneous current and the chemical potential. We find single…