Any-order propagation of the nonlinear Schroedinger equation

We derive an exact propagation scheme for nonlinear Schroedinger equations. This scheme is entirely analogous to the propagation of linear Schroedinger equations. We accomplish this by defining a special operator whose algebraic properties ensure the correct propagation. As applications, we provide a simple proof of a recent conjecture regarding higher-order integrators for the Gross-Pitaevskii equation, extend it to multi-component equations, and to a new class of integrators.Comment: 10 pages, no figures, submitted to Phys. Rev.

Quantum Statistical Calculations and Symplectic Corrector Algorithms

The quantum partition function at finite temperature requires computing the trace of the imaginary time propagator. For numerical and Monte Carlo calculations, the propagator is usually split into its kinetic and potential parts. A higher order splitting will result in a higher order convergent algorithm. At imaginary time, the kinetic energy propagator is usually the diffusion Greens function. Since diffusion cannot be simulated backward in time, the splitting must maintain the positivity of all intermediate time steps. However, since the trace is invariant under similarity transformations of the propagator, one can use this freedom to "correct" the split propagator to higher order. This use of similarity transforms classically give rises to symplectic corrector algorithms. The split propagator is the symplectic kernel and the similarity transformation is the corrector. This work proves a generalization of the Sheng-Suzuki theorem: no positive time step propagators with only kinetic and potential operators can be corrected beyond second order. Second order forward propagators can have fourth order traces only with the inclusion of an additional commutator. We give detailed derivations of four forward correctable second order propagators and their minimal correctors.Comment: 9 pages, no figure, corrected typos, mostly missing right bracket

Finite-size effects on the Hamiltonian dynamics of the XY-model

The dynamical properties of the finite-size magnetization M in the critical region T<T_{KTB} of the planar rotor model on a L x L square lattice are analyzed by means of microcanonical simulations . The behavior of the q=0 structure factor at high frequencies is consistent with field-theoretical results, but new additional features occur at lower frequencies. The motion of M determines a region of spectral lines and the presence of a central peak, which we attribute to phase diffusion. Near T_{KTB} the diffusion constant scales with system size as D ~ L^{-1.6(3)}.Comment: To be published in Europhysics Letter

Calibration of the Ames Anechoic Facility. Phase 1: Short range plan

A calibration was made of the acoustic and aerodynamic characteristics of a small, open-jet wind tunnel in an anechoic room. The jet nozzle was 102 mm diameter and was operated subsonically. The anechoic-room dimensions were 7.6 m by 5.5 m by 3.4 m high (wedge tip to wedge tip). Noise contours in the chamber were determined by various jet speeds and exhaust collector positions. The optimum nozzle/collector separation from an acoustic standpoint was 2.1 m. Jet velocity profiles and turbulence levels were measured using pressure probes and hot wires. The jet was found to be symmetric, with no unusual characteristics. The turbulence measurements were hampered by oil mist contamination of the airflow

Principal Component Analysis with Noisy and/or Missing Data

We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors are more sensitive to the true underlying signal variations rather than being pulled by heteroskedastic measurement noise. Missing data is simply the limiting case of weight=0. The underlying algorithm is a noise weighted Expectation Maximization (EM) PCA, which has additional benefits of implementation speed and flexibility for smoothing eigenvectors to reduce the noise contribution. We present applications of this method on simulated data and QSO spectra from the Sloan Digital Sky Survey.Comment: Accepted for publication in PASP; v2 with minor updates, mostly to bibliograph

Correlation between magnetic and transport properties of phase separated La0.5_{0.5}Ca0.5_{0.5}MnO3_{3}

The effect of low magnetic fields on the magnetic and electrical transport properties of polycrystalline samples of the phase separated compound La$_{0.5}$Ca$_{0.5}$MnO$_{3}$ is studied. The results are interpreted in the framework of the field induced ferromagnetic fraction enlargement mechanism. A fraction expansion coefficient af, which relates the ferromagnetic fraction f with the applied field H, was obtained. A phenomenological model to understand the enlargement mechanism is worked out.Comment: 3 pages, 3 figures, presented at the Fifth LAW-MMM, to appear in Physica B, Minor change

A simulation study of energy transport in the Hamiltonian XY-model

The transport properties of the planar rotator model on a square lattice are analyzed by means of microcanonical and non--equilibrium simulations. Well below the Kosterlitz--Thouless--Berezinskii transition temperature, both approaches consistently indicate that the energy current autocorrelation displays a long--time tail decaying as t^{-1}. This yields a thermal conductivity coefficient which diverges logarithmically with the lattice size. Conversely, conductivity is found to be finite in the high--temperature disordered phase. Simulations close to the transition temperature are insted limited by slow convergence that is presumably due to the slow kinetics of vortex pairs.Comment: Submitted to Journal of Statistical Mechanics: theory and experimen

The Complete Characterization of Fourth-Order Symplectic Integrators with Extended-Linear Coefficients

The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of these {\it extended-linear} symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and non-forward fourth-order algorithms with arbitrary number of operators. Most fourth-order forward integrators can now be derived analytically from this extended-linear formulation without the use of symbolic algebra.Comment: 12 pages, 2 figures, submitted to Phys. Rev. E, corrected typo