1,547 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
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
On Soliton-type Solutions of Equations Associated with N-component Systems
The algebraic geometric approach to -component systems of nonlinear
integrable PDE's is used to obtain and analyze explicit solutions of the
coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to
anti-kink transitions and multi-peaked soliton solutions is carried out.
Transformations are used to connect these solutions to several other equations
that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure
Approximation Algorithms for the Capacitated Domination Problem
We consider the {\em Capacitated Domination} problem, which models a
service-requirement assignment scenario and is also a generalization of the
well-known {\em Dominating Set} problem. In this problem, given a graph with
three parameters defined on each vertex, namely cost, capacity, and demand, we
want to find an assignment of demands to vertices of least cost such that the
demand of each vertex is satisfied subject to the capacity constraint of each
vertex providing the service. In terms of polynomial time approximations, we
present logarithmic approximation algorithms with respect to different demand
assignment models for this problem on general graphs, which also establishes
the corresponding approximation results to the well-known approximations of the
traditional {\em Dominating Set} problem. Together with our previous work, this
closes the problem of generally approximating the optimal solution. On the
other hand, from the perspective of parameterization, we prove that this
problem is {\it W[1]}-hard when parameterized by a structure of the graph
called treewidth. Based on this hardness result, we present exact
fixed-parameter tractable algorithms when parameterized by treewidth and
maximum capacity of the vertices. This algorithm is further extended to obtain
pseudo-polynomial time approximation schemes for planar graphs
Transition from a phase-segregated state to single-phase incommensurate sodium ordering in Na_xCoO_2 with x \approx 0.53
Synchrotron X-ray diffraction investigations of two single crystals of
Na_xCoO_2 from different batches with composition x = 0.525-0.530 reveal
homogeneous incommensurate sodium ordering with propagation vector (0.53 0.53
0) at room-temperature. The incommensurate (qq0) superstructure exists between
220 K and 430 K. The value of q varies between q = 0.514 and 0.529, showing a
broad plateau at the latter value between 260 K and 360 K. On cooling, unusual
reversible phase segregation into two volume fractions is observed. Below 220
K, one volume fraction shows the well-known commensurate orthorhombic x = 0.50
superstructure, while a second volume fraction with x = 0.55 exhibits another
commensurate superstructure, presumably with a 6a x 6a x c hexagonal supercell.
We argue that the commensurate-to-incommensurate transition is an intrinsic
feature of samples with Na concentrations x = 0.5 + d with d ~ 0.03.Comment: Corrected/improved versio
Photon-assisted entanglement creation by minimum-error generalized quantum measurements in the strong coupling regime
We explore possibilities of entangling two distant material qubits with the
help of an optical radiation field in the regime of strong quantum
electrodynamical coupling with almost resonant interaction. For this purpose
the optimum generalized field measurements are determined which are capable of
preparing a two-qubit Bell state by postselection with minimum error. It is
demonstrated that in the strong-coupling regime some of the recently found
limitations of the non-resonant weak-coupling regime can be circumvented
successfully due to characteristic quantum electrodynamical quantum
interference effects. In particular, in the absence of photon loss it is
possible to postselect two-qubit Bell states with fidelities close to unity by
a proper choice of the relevant interaction time. Even in the presence of
photon loss this strong-coupling regime offers interesting perspectives for
creating spatially well-separated Bell pairs with high fidelities, high success
probabilities, and high repetition rates which are relevant for future
realizations of quantum repeaters.Comment: 14 pages, 12 figure
Error tolerance of two-basis quantum key-distribution protocols using qudits and two-way classical communication
We investigate the error tolerance of quantum cryptographic protocols using
-level systems. In particular, we focus on prepare-and-measure schemes that
use two mutually unbiased bases and a key-distillation procedure with two-way
classical communication. For arbitrary quantum channels, we obtain a sufficient
condition for secret-key distillation which, in the case of isotropic quantum
channels, yields an analytic expression for the maximally tolerable error rate
of the cryptographic protocols under consideration. The difference between the
tolerable error rate and its theoretical upper bound tends slowly to zero for
sufficiently large dimensions of the information carriers.Comment: 10 pages, 1 figur
- …