Hamiltonian systems with symmetry, coadjoint orbits and plasma physics

The symplectic and Poisson structures on reduced phase spaces are reviewed, including the symplectic structure on coadjoint orbits of a Lie group and the Lie-Poisson structure on the dual of a Lie algebra. These results are applied to plasma physics. We show in three steps how the Maxwell-Vlasov equations for a collisionless plasma can be written in Hamiltonian form relative to a certain Poisson bracket. First, the Poisson-Vlasov equations are shown to be in Hamiltonian form relative to the Lie-Poisson bracket on the dual of the (nite dimensional) Lie algebra of innitesimal canonical transformations. Then we write Maxwell's equations in Hamiltonian form using the canonical symplectic structure on the phase space of the electromagnetic elds, regarded as a gauge theory. In the last step we couple these two systems via the reduction procedure for interacting systems. We also show that two other standard models in plasma physics, ideal MHD and two- uid electrodynamics, can be written in Hamiltonian form using similar group theoretic techniques

Explanation of the computer listings of Faraday factors for INTASAT users

Using a simplified form of the Appleton-Hartree formula for the phase refractive index, a relationship was obtained between the Faraday rotation angle along the angular path and the total electron content along the vertical path, intersecting the angular at the height of maximum electron density. Using the second mean value theorem of integration, the function B cosine theta second chi was removed from under the integral sign and replaced by a 'mean' value. The mean value factors were printed on the computer listing for 39 stations receiving signals from the INTASAT satellite during the specified time period. The data is presented by station and date. Graphs are included to demonstrate the variation of the Faraday factor with local time and season, with magnetic latitude, elevation and azimuth angles. Other topics discussed include a description of the bent ionospheric model, the earth's magnetic field model, and the sample computer listing

Understanding the dynamical structure of pulsating stars. HARPS spectroscopy of the delta Scuti stars rho Pup and DX Cet

High-resolution spectroscopy is a powerful tool to study the dynamical structure of pulsating stars atmosphere. We aim at comparing the line asymmetry and velocity of the two delta Sct stars rho Pup and DX Cet with previous spectroscopic data obtained on classical Cepheids and beta Cep stars. We obtained, analysed and discuss HARPS high-resolution spectra of rho Pup and DX Cet. We derived the same physical quantities as used in previous studies, which are the first-moment radial velocities and the bi-Gaussian spectral line asymmetries. The identification of f=7.098 (1/d) as a fundamental radial mode and the very accurate Hipparcos parallax promote rho Pup as the best standard candle to test the period-luminosity relations of delta Sct stars. The action of small-amplitude nonradial modes can be seen as well-defined cycle-to-cycle variations in the radial velocity measurements of rho Pup. Using the spectral-line asymmetry method, we also found the centre-of-mass velocities of rho Pup and DX Cet, V_gamma = 47.49 +/- 0.07 km/s and V_gamma = 25.75 +/- 0.06 km/s, respectively. By comparing our results with previous HARPS observations of classical Cepheids and beta Cep stars, we confirm the linear relation between the atmospheric velocity gradient and the amplitude of the radial velocity curve, but only for amplitudes larger than 22.5 km/s. For lower values of the velocity amplitude (i.e., < 22.5 km/s), our data on rho Pup seem to indicate that the velocity gradient is null, but this result needs to be confirmed with additional data. We derived the Baade-Wesselink projection factor p = 1.36 +/- 0.02 for rho Pup and p = 1.39 +/- 0.02 for DX Cet. We successfully extended the period-projection factor relation from classical Cepheids to delta Scuti stars.Comment: Accepted for publication in A&A (in press

Non-linear optomechanical measurement of mechanical motion

Precision measurement of non-linear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of non-linear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator by exploiting the intrinsic non-linearity of the radiation pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100~pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can be used to experimentally explore collapse models of the wavefunction and the potential for mechanical-resonator-based quantum information and metrology applications.Comment: 8 pages, 4 figures, extensive supplementary material available with published versio

Predicting narrow states in the spectrum of a nucleus beyond the proton drip line

Properties of particle-unstable nuclei lying beyond the proton drip line can be ascertained by considering those (usually known) properties of its mirror neutron-rich system. We have used a multi-channel algebraic scattering theory to map the known properties of the neutron-${}^{14}$C system to those of the proton-${}^{14}$O one from which we deduce that the particle-unstable ${}^{15}$F will have a spectrum of two low lying broad resonances of positive parity and, at higher excitation, three narrow negative parity ones. A key feature is to use coupling to Pauli-hindered states in the target.Comment: 5 pages, 3 figure

Continuum coupled cluster expansion

We review the basics of the coupled-cluster expansion formalism for numerical solutions of the many-body problem, and we outline the principles of an approach directed towards an adequate inclusion of continuum effects in the associated single-energy spectrum. We illustrate our findings by considering the simple case of a single-particle quantum mechanics problem.Comment: 16 pages, 1 figur

A construction of Frobenius manifolds with logarithmic poles and applications

A construction theorem for Frobenius manifolds with logarithmic poles is established. This is a generalization of a theorem of Hertling and Manin. As an application we prove a generalization of the reconstruction theorem of Kontsevich and Manin for projective smooth varieties with convergent Gromov-Witten potential. A second application is a construction of Frobenius manifolds out of a variation of polarized Hodge structures which degenerates along a normal crossing divisor when certain generation conditions are fulfilled.Comment: 46 page

Electromagnon excitations in modulated multiferroics

The phenomenological theory of ferroelectricity in spiral magnets presented in [M. Mostovoy, Phys. Rev. Lett. 96, 067601 (2006)] is generalized to describe consistently states with both uniform and modulated-in-space ferroelectric polarizations. A key point in this description is the symmetric part of the magnetoelectric coupling since, although being irrelevant for the uniform component, it plays an essential role for the non-uniform part of the polarization. We illustrate this importance in generic examples of modulated magnetic systems: longitudinal and transverse spin-density wave states and planar cycloidal phase. We show that even in the cases with no uniform ferroelectricity induced, polarization correlation functions follow to the soft magnetic behavior of the system due to the magnetoelectric effect. Our results can be easily generalized for more complicated types of magnetic ordering, and the applications may concern various natural and artificial systems in condensed matter physics (e.g., magnon properties could be extracted from dynamic dielectric response measurements).Comment: 5 page

Towards a microscopic theory of toroidal moments in bulk periodic crystals

We present a theoretical analysis of magnetic toroidal moments in periodic systems, in the limit in which the toroidal moments are caused by a time and space reversal symmetry breaking arrangement of localized magnetic dipole moments. We summarize the basic definitions for finite systems and address the question of how to generalize these definitions to the bulk periodic case. We define the toroidization as the toroidal moment per unit cell volume, and we show that periodic boundary conditions lead to a multivaluedness of the toroidization, which suggests that only differences in toroidization are meaningful observable quantities. Our analysis bears strong analogy to the modern theory of electric polarization in bulk periodic systems, but we also point out some important differences between the two cases. We then discuss the instructive example of a one-dimensional chain of magnetic moments, and we show how to properly calculate changes of the toroidization for this system. Finally, we evaluate and discuss the toroidization (in the local dipole limit) of four important example materials: BaNiF_4, LiCoPO_4, GaFeO_3, and BiFeO_3.Comment: replaced with final (published) version, which includes some changes in the text to improve the clarity of presentatio