Related papers: No free lunch for effective potentials: general co…
We analyze the application of the "tridiagonal representation approach" (TRA) to the Schr\"{o}dinger equation for some simple, exactly-solvable, quantum-mechanical models. In the case of the Kratzer-Fues potential the mathematical reasoning…
The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs…
We study electromagnetic properties of periodic composite structures, such as photonic crystals, involving lossy components. We show that in many cases a properly designed periodic structure can dramatically suppress the losses associated…
Coarse-grained spin density functional theory (SDFT) is a version of SDFT which works with number/spin densities specified to a limited resolution --- averages over cells of a regular spatial partition --- and external potentials constant…
When seeking a numerical representation of a quantum-mechanical multiparticle problem it is tempting to replace a singular short-range interaction by a smooth finite-range pseudopotential. Finite basis set expansions, e.g.~in Fock space,…
Every measurable function f on the circle can be represented as a sum of harmonics with positive spectrum, converging in measure. For convergence almost everywhere this is not true. We discuss several other subsets of Z for which one might…
Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…
Complementarity restricts the accuracy with which incompatible quantum observables can be jointly measured. Despite popular conception, the Heisenberg uncertainty relation does not quantify this principle. We report the experimental…
All living cells transport molecules and ions across membranes, often against concentration gradients. This active transport requires continual energy expenditure and is clearly a nonequilibrium process for which standard equilibrium…
Being able to interpret, or explain, the predictions made by a machine learning model is of fundamental importance. This is especially true when there is interest in deploying data-driven models to make high-stakes decisions, e.g. in…
We present a constructive solution to the N-representability problem---a full characterization of the conditions for constraining the two-electron reduced density matrix (2-RDM) to represent an N-electron density matrix. Previously known…
In multiwinner approval voting, forming a committee that proportionally represents voters' approval ballots is an essential task. The notion of justified representation (JR) demands that any large "cohesive" group of voters should be…
One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to…
We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full group of an ample groupoid being amenable as well as…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
Background: One important ingredient for many applications of nuclear physics to astrophysics, nuclear energy, and stockpile stewardship are cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often…
Using the monodromy method, a compact expression is obtained for the identity block contribution to the expectation value of two low-energy probe operators on a broad class of time-dependent heavy pure states in large-$c$ 2d CFTs. It will…
We investigate the existence and properties of effective potentials in time-dependent density functional theory. We outline conditions for a general solution of the corresponding Sturm-Liouville boundary value problems. We define the set of…
The general structure of the representation theory of a $Z_2$-graded coalgebra is discussed. The result contains the structure of Fourier analysis on compact supergroups and quantisations thereof as a special case. The general linear…
This is a review and tutorial paper which discusses the fundamental limitations on the maximal power which can be received, absorbed, and scattered by an electrically small electrically polarizable particle and infinite periodical arrays of…