Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion

We study the algebra Sp(n,R) of the symplectic model, in particular for the cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we derive a set of partial differential equations for the generators as functions of classical canonical variables. We obtain a solution to these equations that represents the classical limit of a boson mapping of the algebra. The relationship to the collective dynamics is formulated as a theorem that associates the mapping with an exact solution of the time-dependent Hartree approximation. This solution determines a decoupled classical symplectic manifold, thus satisfying the criteria that define an exactly solvable model in the theory of large amplitude collective motion. The models thus obtained also provide a test of methods for constructing an approximately decoupled manifold in fully realistic cases. We show that an algorithm developed in one of our earlier works reproduces the main results of the theorem.Comment: 23 pages, LaTeX using REVTeX 3.

Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles

We consider free lattice fermions subjected to a static bounded potential and a time- and space-dependent electric field. For any bounded convex region $\mathcal{R}\subset \mathbb{R}^{d}$ ($d\geq 1$) of space, electric fields $\mathcal{E}$ within $\mathcal{R}$ drive currents. At leading order, uniformly with respect to the volume $\left| \mathcal{R}\right|$ of $\mathcal{R}$ and the particular choice of the static potential, the dependency on $\mathcal{E}$ of the current is linear and described by a conductivity distribution. Because of the positivity of the heat production, the real part of its Fourier transform is a positive measure, named here (microscopic) conductivity measure of $\mathcal{R}$, in accordance with Ohm's law in Fourier space. This finite measure is the Fourier transform of a time-correlation function of current fluctuations, i.e., the conductivity distribution satisfies Green-Kubo relations. We additionally show that this measure can also be seen as the boundary value of the Laplace-Fourier transform of a so-called quantum current viscosity. The real and imaginary parts of conductivity distributions satisfy Kramers-Kronig relations. At leading order, uniformly with respect to parameters, the heat production is the classical work performed by electric fields on the system in presence of currents. The conductivity measure is uniformly bounded with respect to parameters of the system and it is never the trivial measure $0\,\mathrm{d}\nu$. Therefore, electric fields generally produce heat in such systems. In fact, the conductivity measure defines a quadratic form in the space of Schwartz functions, the Legendre-Fenchel transform of which describes the resistivity of the system. This leads to Joule's law, i.e., the heat produced by currents is proportional to the resistivity and the square of currents

25 kHz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity

We report on the spectral properties of a diode laser with a tunable external cavity in integrated optics. Even though the external cavity is short compared to other small-bandwidth external cavity lasers, the spectral bandwidth of this tunable laser is as small as 25 kHz (FWHM), at a side-mode suppression ratio (SMSR) of 50 dB. Our laser is also able to access preset wavelengths in as little as 200 us and able to tune over the full telecom C-band (1530 nm - 1565 nm).Comment: 8 pages, 7 figure

Interplanetary propulsion using inertial fusion

Inertial fusion can be used to power spacecraft within the solar system and beyond. Such spacecraft have the potential for short-duration manned-mission performance exceeding other technologies. We are conducting a study to assess the systems aspects of inertial fusion as applied to such missions, based on the conceptual engine design of Hyde (1983) we describe the required systems for an entirely new spacecraft design called VISTA that is based on the use of DT fuel. We give preliminary design details for the power conversion and power conditioning systems for manned missions to Mars of total duration of about 100 days. Specific mission performance results will be published elsewhere, after the study has been completed

Observation of Leggett's collective mode in a multi-band MgB2 superconductor

We report observation of Leggett's collective mode in a multi-band MgB2 superconductor with T_c=39K arising from the fluctuations in the relative phase between two superconducting condensates. The novel mode is observed by Raman spectroscopy at 9.4 meV in the fully symmetric scattering channel. The observed mode frequency is consistent with theoretical considerations based on the first principle computations.Comment: Accepted for PR

An O(n^3)-Time Algorithm for Tree Edit Distance

The {\em edit distance} between two ordered trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this paper, we present a worst-case $O(n^3)$-time algorithm for this problem, improving the previous best $O(n^3\log n)$-time algorithm~\cite{Klein}. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems (which is interesting in its own right), together with a deeper understanding of the previous algorithms for the problem. We also prove the optimality of our algorithm among the family of \emph{decomposition strategy} algorithms--which also includes the previous fastest algorithms--by tightening the known lower bound of $\Omega(n^2\log^2 n)$~\cite{Touzet} to $\Omega(n^3)$, matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds of $\Theta(n m^2 (1 + \log \frac{n}{m}))$ when the two trees have different sizes $m$ and~$n$, where $m < n$.Comment: 10 pages, 5 figures, 5 .tex files where TED.tex is the main on

CLAS+FROST: new generation of photoproduction experiments at Jefferson Lab

A large part of the experimental program in Hall B of the Jefferson Lab is dedicated to baryon spectroscopy. Photoproduction experiments are essential part of this program. CEBAF Large Acceptance Spectrometer (CLAS) and availability of circularly and linearly polarized tagged photon beams provide unique conditions for this type of experiments. Recent addition of the Frozen Spin Target (FROST) gives a remarkable opportunity to measure double and triple polarization observables for different pseudo-scalar meson photoproduction processes. For the first time, a complete or nearly complete experiment becomes possible and will allow model independent extraction of the reaction amplitude. An overview of the experiment and its current status is presented.Comment: 6 pages, 7 figures. Invited paper NSTAR 2009 conferenc