1,104 research outputs found
Simple expressions for the long walk distance
The walk distances in graphs are defined as the result of appropriate
transformations of the proximity measures, where
is the weighted adjacency matrix of a connected weighted graph and is a
sufficiently small positive parameter. The walk distances are graph-geodetic,
moreover, they converge to the shortest path distance and to the so-called long
walk distance as the parameter approaches its limiting values. In this
paper, simple expressions for the long walk distance are obtained. They involve
the generalized inverse, minors, and inverses of submatrices of the symmetric
irreducible singular M-matrix where is the Perron
root of Comment: 7 pages. Accepted for publication in Linear Algebra and Its
Application
Vortex structures of rotating spin-orbit coupled Bose-Einstein condensates
We consider the quasi-2D two-component Bose-Einstein condensates with Rashba
spin-orbit (SO) coupling in a rotating trap. An external Zeeman term favoring
spin polarization along the radial direction is also considered, which has the
same form as the non-canonical part of the mechanical angular momentum. The
rotating condensate exhibits rich structures as varying the strengths of
trapping potential and interaction. With a strong trapping potential, the
condensate exhibits a half-quantum vortex-lattice configuration. Such a
configuration is driven to the normal one by introducing the external radial
Zeeman field. In the case of a weak trap potential, the condensate exhibits a
multi-domain pattern of plane-wave states under the external radial Zeeman
field.Comment: 8 pages, 7 figures, two figures are adde
Incidence matrix games
We consider the two-person zero-sum game in which the strategy sets for Players I and II consist of the vertices and the edges of a directed graph respectively.If Player I chooses vertex v and Player II chooses edge e; then the payoff is zero if v and e are not incident and otherwise it is 1 or _1 according as e originates or terminates at v: We obtain an explicit expression for the value of this game and describe the structure of optimal strategies.A similar problem is considered for undirected graphs and it is shown to be related to the theory of 2-matchings in graphs.
Imprinting a complete information about a quantum channel on its output state
We introduce a novel property of bipartite quantum states, which we call
"faithfulness", and we say that a state is faithful when acting with a channel
on one of the two quantum systems, the output state carries a complete
information about the channel. The concept of faithfulness can also be extended
to sets of states, when the output states patched together carry a complete
imprinting of the channel.Comment: revtex4, 4 pages, submitted to PR
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