Reducible Correlations in Dicke States

We apply a simple observation to show that the generalized Dicke states can be determined from their reduced subsystems. In this framework, it is sufficient to calculate the expression for only the diagonal elements of the reudced density matrices in terms of the state coefficients. We prove that the correlation in generalized Dicke states $|GD_N^{(\ell)}>$ can be reduced to $2\ell$-partite level. Application to the Quantum Marginal Problem is also discussed.Comment: 12 pages, single column; accepted in J. Phys. A as FT

Failure of Thiocyanate to Influence The Flux of Sodium Through The Isolated Frog Gastric Mucosa

Isolated stomachs from mammals showed substantial active absorption of sodium (Am.J. Dig. Dis. 14:221-238, 1969) in contrast to isolated frog gastric mucosa. Could the difference have been due to a micro-environment in the latter preparation based on fine structure features that maintained high H-ion concentration at the site of active transport? To answer this, H-ion secretion was inhibited in frog gastric mucosa with 15 mM thiocyanate. Unidirectional fluxes of sodium were not materially affected. These results cast doubt on a possible depression of active sodium absorption by a high H-ion concentration in the microenvironment of the isolated amphibian mucosa

The doubly negative matrix completion problem

An $n\times n$ matrix over the field of real numbers is a doubly negative matrix if it is symmetric, negative definite and entry-wise negative. In this paper, we are interested in the doubly negative matrix completion problem, that is when does a partial matrix have a doubly negative matrix completion. In general, we cannot guarantee the existence of such a completion. In this paper, we prove that every partial doubly negative matrix whose associated graph is a $p$-chordal graph $G$ has a doubly negative matrix completion if and only if $p=1$. Furthermore, the question of completability of partial doubly negative matrices whose associated graphs are cycles is addressed.Spanish DGI - BFM2001-0081-C03-02.Fundação para a Ciência e a Tecnologia (FCT) – Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI)

Signatures of partition functions and their complexity reduction through the KP II equation

A statistical amoeba arises from a real-valued partition function when the positivity condition for pre-exponential terms is relaxed, and families of signatures are taken into account. This notion lets us explore special types of constraints when we focus on those signatures that preserve particular properties. Specifically, we look at sums of determinantal type, and main attention is paid to a distinguished class of soliton solutions of the Kadomtsev-Petviashvili (KP) II equation. A characterization of the signatures preserving the determinantal form, as well as the signatures compatible with the KP II equation, is provided: both of them are reduced to choices of signs for columns and rows of a coefficient matrix, and they satisfy the whole KP hierarchy. Interpretations in term of information-theoretic properties, geometric characteristics, and the relation with tropical limits are discussed.Comment: 42 pages, 11 figures. Section 7.1 has been added, the organization of the paper has been change

Algebraic inversion of the Dirac equation for the vector potential in the non-abelian case

We study the Dirac equation for spinor wavefunctions minimally coupled to an external field, from the perspective of an algebraic system of linear equations for the vector potential. By analogy with the method in electromagnetism, which has been well-studied, and leads to classical solutions of the Maxwell-Dirac equations, we set up the formalism for non-abelian gauge symmetry, with the SU(2) group and the case of four-spinor doublets. An extended isospin-charge conjugation operator is defined, enabling the hermiticity constraint on the gauge potential to be imposed in a covariant fashion, and rendering the algebraic system tractable. The outcome is an invertible linear equation for the non-abelian vector potential in terms of bispinor current densities. We show that, via application of suitable extended Fierz identities, the solution of this system for the non-abelian vector potential is a rational expression involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial vector current densities, albeit in the non-closed form of a Neumann series.Comment: 21pp, uses iopar

Parameters Related to Tree-Width, Zero Forcing, and Maximum Nullity of a Graph

Tree-width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by a graph. We establish relationships between these parameters, including several Colin de Verdière type parameters, and introduce numerous variations, including the minor monotone floors and ceilings of some of these parameters. This leads to new graph parameters and to new characterizations of existing graph parameters. In particular, tree-width, largeur d\u27arborescence, path-width, and proper path-width are each characterized in terms of a minor monotone floor of a certain zero forcing parameter defined by a color change rule

The principal rank characteristic sequence over various fields

Given an n x n matrix, its principal rank characteristic sequence is a sequence of length n+1 of 0s and 1s where, for k = 0, 1, . . . , n, a 1 in the kth position indicates the existence of a principal submatrix of rank k and a 0 indicates the absence of such a submatrix. The principal rank characteristic sequences for symmetric matrices over various fields are investigated, with all such attainable sequences determined for all n over any field with characteristic 2. A complete list of attainable sequences for real symmetric matrices of order 7 is reported