385,868 research outputs found
Catalytic majorization and norms
An important problem in quantum information theory is the mathematical
characterization of the phenomenon of quantum catalysis: when can the
surrounding entanglement be used to perform transformations of a jointly held
quantum state under LOCC (local operations and classical communication) ?
Mathematically, the question amounts to describe, for a fixed vector , the
set of vectors such that we have for
some , where denotes the standard majorization relation. Our main
result is that the closure of in the norm can be fully
described by inequalities on the norms: for all
. This is a first step towards a complete description of
itself. It can also be seen as a -norm analogue of Ky Fan dominance
theorem about unitarily invariant norms. The proofs exploits links with another
quantum phenomenon: the possibiliy of multiple-copy transformations
( for given ). The main new tool is a
variant of Cram\'er$ theorem on large deviations for sums of i.i.d. random
variables
HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part II. Optimization of the Runge-Kutta smoother
Using a detailed multilevel analysis of the complete hp-Multigrid as Smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator. This multilevel analysis is used to optimize the coefficients in the semi-implicit Runge-Kutta smoother, such that the spectral radius of the multigrid error transformation operator is minimal under properly chosen constraints. The Runge-Kutta coefficients for a wide range of cell Reynolds numbers and a detailed analysis of the performance of the hp-MGS algorithm are presented. In addition, the computational complexity of the hp-MGS algorithm is investigated. The hp-MGS algorithm is tested on a fourth order accurate space-time discontinuous Galerkin finite element discretization of the advection-diffusion equation for a number of model problems, which include thin boundary layers and highly stretched meshes, and a non-constant advection velocity. For all test cases excellent multigrid convergence is obtained
Super Landau Models on Odd Cosets
We construct d=1 sigma models of the Wess-Zumino type on the SU(n|1)/U(n)
fermionic cosets. Such models can be regarded as a particular supersymmetric
extension (with a target space supersymmetry) of the classical Landau model,
when a charged particle possesses only fermionic coordinates. We consider both
classical and quantum models, and prove the unitarity of the quantum model by
introducing the metric operator on the Hilbert space of the quantum states,
such that all their norms become positive-definite. It is remarkable that the
quantum n=2 model exhibits hidden SU(2|2) symmetry. We also discuss the planar
limit of these models. The Hilbert space in the planar n=2 case is shown to
carry SU(2|2) symmetry which is different from that of the SU(2|1)/U(1) model.Comment: 1 + 33 pages, some typos correcte
A contribution to the Aleksandrov conservative distance problem in two dimensions
Let be a two-dimensional real normed space. In this paper we show that if
the unit circle of does not contain any line segment such that the distance
between its endpoints is greater than 1, then every transformation which preserves the unit distance is automatically an affine isometry.
In particular, this condition is satisfied when the norm is strictly convex.Comment: 8 pages, 3 figure
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