Search results for "combinatoric"
showing 10 items of 1776 documents
Diverging exchange force and form of the exact density matrix functional
2019
For translationally invariant one-band lattice models, we exploit the ab initio knowledge of the natural orbitals to simplify reduced density matrix functional theory (RDMFT). Striking underlying features are discovered: First, within each symmetry sector, the interaction functional $\mathcal{F}$ depends only on the natural occupation numbers $\bf{n}$. The respective sets $\mathcal{P}^1_N$ and $\mathcal{E}^1_N$ of pure and ensemble $N$-representable one-matrices coincide. Second, and most importantly, the exact functional is strongly shaped by the geometry of the polytope $\mathcal{E}^1_N \equiv \mathcal{P}^1_N $, described by linear constraints $D^{(j)}(\bf{n})\geq 0$. For smaller systems,…
Efficiencies of logical Bell measurements on Calderbank-Shor-Steane codes with static linear optics
2019
We show how the efficiency of a logical Bell measurement (BM) can be calculated for arbitrary Calderbank-Shor-Steane (CSS) codes with the experimentally important constraint of using only transversal static linear-optical BMs on the physical single-photon qubit level. For this purpose, we utilize the codes' description in terms of stabilizers in order to calculate general efficiencies for the loss-free case, but also for specific cases including photon loss. These efficiencies can be, for instance, used for obtaining transmission rates of all-optical quantum repeaters. In the loss-free case, we demonstrate that the important class of CSS codes with identical physical-qubit support for the t…
Feynman graph polynomials
2010
The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.
Experiments on the Parallel Hall Effect in Three-Dimensional Metamaterials
2017
The usual Hall effect in a semiconductor leads to a voltage perpendicular to an applied static magnetic field. The authors significantly extend their recent work and demonstrate $e\phantom{\rule{0}{0ex}}x\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}y$ that not only the sign but also the direction of the Hall field can be tailored by a metamaterial's microstructure. They show that, with judicious engineering, the Hall voltage can be $p\phantom{\rule{0}{0…
Combinatorial Models in the Topological Classification of Singularities of Mappings
2018
The topological classification of finitely determined map germs \(f:(\mathbb R^n,0)\rightarrow (\mathbb R^p,0)\) is discrete (by a theorem due to R. Thom), hence we want to obtain combinatorial models which codify all the topological information of the map germ f. According to Fukuda’s work, the topology of such germs is determined by the link, which is obtained by taking the intersection of the image of f with a small enough sphere centered at the origin. If \(f^{-1}(0)=\{0\}\), then the link is a topologically stable map \(\gamma :S^{n-1}\rightarrow S^{p-1}\) (or stable if (n, p) are nice dimensions) and f is topologically equivalent to the cone of \(\gamma \). When \(f^{-1}(0)\ne \{0\}\)…
A Remark on an Overdetermined Problem in Riemannian Geometry
2016
Let (M, g) be a Riemannian manifold with a distinguished point O and assume that the geodesic distance d from O is an isoparametric function. Let \(\varOmega \subset M\) be a bounded domain, with \(O \in \varOmega \), and consider the problem \(\varDelta _p u = -1\ \mathrm{in}\ \varOmega \) with \(u=0\ \mathrm{on}\ \partial \varOmega \), where \(\varDelta _p\) is the p-Laplacian of g. We prove that if the normal derivative \(\partial _{\nu }u\) of u along the boundary of \(\varOmega \) is a function of d satisfying suitable conditions, then \(\varOmega \) must be a geodesic ball. In particular, our result applies to open balls of \(\mathbb {R}^n\) equipped with a rotationally symmetric metr…
Parabolic equations with natural growth approximated by nonlocal equations
2017
In this paper we study several aspects related with solutions of nonlocal problems whose prototype is $$ u_t =\displaystyle \int_{\mathbb{R}^N} J(x-y) \big( u(y,t) -u(x,t) \big) \mathcal G\big( u(y,t) -u(x,t) \big) dy \qquad \mbox{ in } \, \Omega \times (0,T)\,, $$ being $ u (x,t)=0 \mbox{ in } (\mathbb{R}^N\setminus \Omega )\times (0,T)\,$ and $ u(x,0)=u_0 (x) \mbox{ in } \Omega$. We take, as the most important instance, $\mathcal G (s) \sim 1+ \frac{\mu}{2} \frac{s}{1+\mu^2 s^2 }$ with $\mu\in \mathbb{R}$ as well as $u_0 \in L^1 (\Omega)$, $J$ is a smooth symmetric function with compact support and $\Omega$ is either a bounded smooth subset of $\mathbb{R}^N$, with nonlocal Dirichlet bound…
An invariant analytic orthonormalization procedure with applications
2007
We apply the orthonormalization procedure previously introduced by two of us and adopted in connection with coherent states to Gabor frames and other examples. For instance, for Gabor frames we show how to construct $g(x)\in L^2(\Bbb{R})$ in such a way the functions $g_{\underline n}(x)=e^{ian_1x}g(x+an_2)$, $\underline n\in\Bbb{Z}^2$ and $a$ some positive real number, are mutually orthogonal. We discuss in some details the role of the lattice naturally associated to the procedure in this analysis.
Measurements of the Absolute Branching Fractions of B±→K±Xcc̅
2006
We study the two-body decays of ${B}^{\ifmmode\pm\else\textpm\fi{}}$ mesons to ${K}^{\ifmmode\pm\else\textpm\fi{}}$ and a charmonium state ${X}_{c\overline{c}}$ in a sample of $210.5\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data from the BABAR experiment. We perform measurements of absolute branching fractions $\mathcal{B}({B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{K}^{\ifmmode\pm\else\textpm\fi{}}{X}_{c\overline{c}})$ using a missing mass technique, and report several new or improved results. In particular, the upper limit $\mathcal{B}\mathbf{(}{B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{K}^{\ifmmode\pm\else\textpm\fi{}}X(3872)\mathbf{)}l3.2\ifmmode…
Precision thrust cumulant moments atN3LL
2012
We consider cumulant moments (cumulants) of the thrust distribution using predictions of the full spectrum for thrust including O(alpha_s^3) fixed order results, resummation of singular N^3LL logarithmic contributions, and a class of leading power corrections in a renormalon-free scheme. From a global fit to the first thrust moment we extract the strong coupling and the leading power correction matrix element Omega_1. We obtain alpha_s(m_Z) = 0.1141 \pm (0.0004)_exp \pm (0.0014)_hadr \pm (0.0007)_pert, where the 1-sigma uncertainties are experimental, from hadronization (related to Omega_1) and perturbative, respectively, and Omega_1 = 0.372 \pm (0.044)_exp \pm (0.039)_pert GeV. The n-th th…