1,206 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
Energy dependent Schrödinger operators and complex Hamiltonian systems on Riemann surfaces
We use so-called energy-dependent Schrödinger operators to establish a link between special classes of solutions on N-component systems of evolution equations and finite dimensional Hamiltonian systems on the moduli spaces of Riemann surfaces. We also investigate the phase-space geometry of these Hamiltonian systems and introduce deformations of the level sets associated to conserved quantities, which results in a new class of solutions with monodromy for N-component systems of PDEs.
After constructing a variety of mechanical systems related to the spatial flows of nonlinear evolution equations, we investigate their semiclassical limits. In particular, we obtain semicalssical asymptotics for the Bloch eigenfunctions of the energy dependent Schrödinger operators, which is of importance in investigating zero-dispersion limits of N-component systems of PDEs
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
Maximum Entanglement in Squeezed Boson and Fermion States
A class of squeezed boson and fermion states is studied with particular
emphasis on the nature of entanglement. We first investigate the case of
bosons, considering two-mode squeezed states. Then we construct the fermion
version to show that such states are maximum entangled, for both bosons and
fermions. To achieve these results, we demonstrate some relations involving
squeezed boson states. The generalization to the case of fermions is made by
using Grassmann variables.Comment: 4 page
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
Elastic Interfacial Waves in Discrete and Continuous Media
Phonon spectra of bicrystals with relaxed grain-boundary structure display a variety of localized modes including long-wavelength acoustic modes. Continuum solutions for localized waves that incorporate atomic-level elastic properties of the interface via discontinuity relations agree well with the latter modes. In contrast, classical solutions that depend only on bulk elastic properties do not. This demonstrates that the distinct atomic structure of the interface is a controlling factor, and it is shown how local, atomic-level properties can be incorporated into continuum analyses of interfacial phenomena
Measurement induced chaos with entangled states
The dynamics of an ensemble of identically prepared two-qubit systems is
investigated which is subjected to the iteratively applied measurements and
conditional selection of a typical entanglement purification protocol. It is
shown that the resulting measurement-induced non-linear dynamics of the
two-qubit state exhibits strong sensitivity to initial conditions and also true
chaos. For a special class of initially prepared two-qubit states two types of
islands characterize the asymptotic limit. They correspond to a separable and a
maximally entangled two-qubit state, respectively, and their boundaries form
fractal-like structures. In the presence of incoherent noise an additional
stable asymptotic cycle appears.Comment: 5 pages, 3 figure
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