Related papers: Atoms and charge in type $C_2$
All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that Hamilton-Jacobi equation and Klein-Gordon-Fock equation for a charged test particle can be integrated by the method of complete…
Two-dimensional crystals on curved manifolds exhibit nontrivial defect structures. Here, we consider "active crystals" on a sphere, which are composed of self-propelled colloidal particles. Our work is based on a new…
Suppose that $X\_{1}$ and $X\_{2}$ are two selfadjoint random variables that are freely independent over an operator algebra $\mathcal{B}$. We describe the possible operator atoms of the distribution of $X\_{1}+X\_{2}$ and, using…
We introduce constellation ensembles, in which charged particles on a line (or circle) are linked with charged particles on parallel lines (or concentric circles). We present formulas for the partition functions of these ensembles in terms…
The processes of generation of phonons and electron excitations with quantum oriented particle in crystal are considered. Expressions are obtained for the probability of emission of phonons and plasmons with channeled particle. The theory…
Radiative corrections to electronic structure are characterized by perturbative expansions in $\alpha$ and $Z\alpha$, where $\alpha$ is the fine-structure constant and $Z$ is the nuclear charge. A formulation of the leading-order…
Long-range interactions and electric response are essential for accurate modeling of condensed-phase systems, but capturing them efficiently remains a challenge for atomistic machine learning. Traditionally, these two phenomena can be…
This paper addresses the decomposition number problem for spin representations of symmetric groups in odd characteristic. Our main aim is to find a combinatorial formula for decomposition numbers in blocks of defect $2$, analogous to…
A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material…
Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter,…
For the first time a method is devised for non-iterative modeling of motion of a radiating, electrified pointlike mass that has an internal structure. New, supplementary kinetic constants of accelerated charged particles are defined, that…
We present a novel derivation of the original Levitov formula, for the statistics of charge transported between electron reservoirs. This is done by proving a trace formula, which relates certain traces in Fock space to single particle…
We develop several techniques for the study of the radical ideal $I$ defining the diagonal locus of $(\C^2)^n$. Using these techniques, we give combinatorial construction of generators for $I$ of certain bi-degrees.
Standard X-ray crystallography methods use free-atom models to calculate mean unit cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a…
We analyse a notion of $C^*$-independence for $\mathbb{Z}_2$-graded $C^*$-algebras. We provide other notions of statistical independence for $\mathbb{Z}_2$-graded von Neumann algebras and prove some relationships between them. We provide a…
We study an algebra spanned by modified Kostka polynomials. Particular structure coefficients of this algebra are interpreted as traces of some Weyl group actions on the intersection cohomology of comet-shaped quiver varieties.
We define highest weight categorical actions of sl_2 on highest weight categories and show that basically all known examples of categorical sl_2-actions on highest weight categories (including rational and polynomial representations of…
We study systems that approach a state possessing discrete symmetry due to different degenerate realizations for the system. For concreteness, we consider fractionally filled systems where degeneracy comes from the presence of identical…
How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a…
Recent optical-potential studies of the phenomenology of kaonic atoms are reviewed. It is shown that the data can be fitted by a complex optical potential with either a relatively shallow attractive component (about -50 MeV at…