Related papers: Extremal subsets and atom-positivity

In this note, inspired by the proof of the Kirillov-Reshetikhin conjecture, we consider tensor products of Kirillov-Reshetikhin modules of a fixed node and various level. We fix a positive integer and attach to each of its partitions such a…

The Lifshitz-type formulas for the free energy and Casimir-Polder force acting between an atom possessing a permanent magnetic moment and a wall made of different materials are derived. Simple model allowing analytic results is considered…

We perform computational studies of jammed particle packings in two dimensions undergoing isotropic compression using the well-characterized soft particle (SP) model and the deformable particle (DP) model that we developed for compressed…

We study properties that allow first-order theories to be disjointly combined, including stable infiniteness, shininess, strong politeness, and gentleness. Specifically, we describe a Galois connection between sets of decidable theories,…

Kang et al. provided a path realization of the crystal graph of a highest weight module over a quantum affine algebra, as certain semi-infinite tensor products of a single perfect crystal. In this paper, this result is generalized to give a…

Here we present an approach to the problem of superradiance in dense atomic samples, when dipolar interactions arise between atoms. Our treatment consists of the sequential use of the Holstein-Primakoff and mean-field approximations, from…

Given a collection of K\"ahler forms and a continuous weight on a compact complex manifold we show that it is possible to define natural new notions of extremal potentials and equilibrium measures which coincide with classical notions when…

The study of exotic nuclei---nuclei with the ratio of neutron number $N$ to proton number $Z$ deviating much from that of those found in nature---is at the forefront of nuclear physics research because it can not only reveal novel nuclear…

We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove…

Let $\mathfrak{g}$ be a hyperbolic Kac-Moody algebra of rank 2, and set $\lambda=\Lambda_{1} - \Lambda_{2}$, where $\Lambda_{1}$, $\Lambda_{2}$ are the fundamental weights. Denote by $V(\lambda)$ the extremal weight module of extremal…

High values of deuterium compressibility under shock-wave compression, recently discovered in several experiments, are explained by an unusual dielectric-metal phase transition from a dense molecular gas into a liquid-metal atomic gas. This…

We address the study of the thermodynamics of a crystalline solid by applying q-deformed algebras. We based part of our study by considering both Einstein and Debye models. We have mainly explored the q-deformed thermal and electric…

Two-dimensional Rydberg atoms are modeled at low temperatures by means of the classical Monte Carlo method. The Coulomb repulsion of charged ions competing with the repulsive van der Waals long-range tail is modeled by a number of…

We study numerically the behaviour of a mixture of a passive isotropic fluid and an active polar gel, in the presence of a surfactant favouring emulsification. Focussing on parameters for which the underlying free energy favours the…

We formulate a strong positivity conjecture on characters afforded by the Alvis-Curtis dual of the intersection cohomology of Deligne-Lusztig varieties. This conjecture provides a powerful tool to determine decomposition numbers of…

We describe a particular class of pairs of quantum observables which are extremal in the convex set of all pairs of compatible quantum observables. The pairs in this class are constructed as uniformly noisy versions of two mutually unbiased…

Let $\mathbf{U}$ be a quantum group of symmetric type. We introduce the {\it thickening realization} to realize (a suitable approximation of) the tensor product ${^{\omega}\Lambda_{\lambda_1}}\otimes \Lambda_{\lambda_2}$ of a simple…

Dipolar quantum droplets are exotic quantum objects that are self-bound due to the subtle balance of attraction, repulsion and quantum correlations. Here we present a systematic study of the critical atom number of these self-bound…

Our object of study is extremal functions which are defined by distance functions of convex bodies. These functions take values in the moduli spaces of algebraic and geometric objects associated with these ${\mathbb Z}$-modules (geometric…

In this paper, we provide a complete description of the minimal primes of ideals generated by adjacent $2$-minors, in terms of the so-called admissible sets and associated lattice ideals. We prove that for these ideals, the properties of…