2,329 research outputs found
Resonant Geometric Phases for Soliton Equations
The goal of the present paper is to introduce a multidimensional generalization of asymptotic reduction given in a paper by Alber and Marsden [1992], to use this to obtain a new class of solutions that we call resonant solitons, and to study the corresponding geometric phases. The term "resonant solitons" is used because those solutions correspond to a spectrum with multiple points, and they also represent a dividing solution between two different types of solitons. In this sense, these new solutions are degenerate and, as such, will be considered as singular points in the moduli space of solitons
Random unitary dynamics of quantum networks
We investigate the asymptotic dynamics of quantum networks under repeated
applications of random unitary operations. It is shown that in the asymptotic
limit of large numbers of iterations this dynamics is generally governed by a
typically low dimensional attractor space. This space is determined completely
by the unitary operations involved and it is independent of the probabilities
with which these unitary operations are applied. Based on this general feature
analytical results are presented for the asymptotic dynamics of arbitrarily
large cyclic qubit networks whose nodes are coupled by randomly applied
controlled-NOT operations.Comment: 4 pages, 2 figure
Completely positive covariant two-qubit quantum processes and optimal quantum NOT operations for entangled qubit pairs
The structure of all completely positive quantum operations is investigated
which transform pure two-qubit input states of a given degree of entanglement
in a covariant way. Special cases thereof are quantum NOT operations which
transform entangled pure two-qubit input states of a given degree of
entanglement into orthogonal states in an optimal way. Based on our general
analysis all covariant optimal two-qubit quantum NOT operations are determined.
In particular, it is demonstrated that only in the case of maximally entangled
input states these quantum NOT operations can be performed perfectly.Comment: 14 pages, 2 figure
Characterization of distillability of entanglement in terms of positive maps
A necessary and sufficient condition for 1-distillability is formulated in
terms of decomposable positive maps. As an application we provide insight into
why all states violating the reduction criterion map are distillable and
demonstrate how to construct such maps in a systematic way. We establish a
connection between a number of existing results, which leads to an elementary
proof for the characterisation of distillability in terms of 2-positive maps.Comment: 4 pages, revtex4. Published revised version, title changed, expanded
discussion, main result unchange
Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians
The algebraic-geometric approach is extended to study solutions of
N-component systems associated with the energy dependent Schrodinger operators
having potentials with poles in the spectral parameter, in connection with
Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems
under study include the shallow water equation and Dym type equation. The
classes of solutions are described in terms of theta-functions and their
singular limits by using new parameterizations. A qualitative description of
real valued solutions is provided
Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media
We analyze frequency conversion and its control among three light waves using a geometric approach that enables the dynamics of the waves to be visualized on a closed surface in three dimensions. It extends the analysis based on the undepleted-pump linearization and provides a simple way to understand the fully nonlinear dynamics. The Poincaré sphere has been used in the same way to visualize polarization dynamics. A geometric understanding of control strategies that enhance energy transfer among interacting waves is introduced, and the quasi-phase-matching strategy that uses microstructured quadratic materials is illustrated in this setting for both type I and II second-harmonic generation and for parametric three-wave interactions
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