1,237 research outputs found
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 can be reduced to
-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 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 -chordal graph has a doubly
negative matrix completion if and only if . 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
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