Chaoticity without thermalisation in disordered lattices

We study chaoticity and thermalization in Bose-Einstein condensates in disordered lattices, described by the discrete nonlinear Schr\"odinger equation (DNLS). A symplectic integration method allows us to accurately obtain both the full phase space trajectories and their maximum Lyapunov exponents (mLEs), which characterize their chaoticity. We find that disorder destroys ergodicity by breaking up phase space into subsystems that are effectively disjoint on experimentally relevant timescales, even though energetically, classical localisation cannot occur. This leads us to conclude that the mLE is a very poor ergodicity indicator, since it is not sensitive to the trajectory being confined to a subregion of phase space. The eventual thermalization of a BEC in a disordered lattice cannot be predicted based only on the chaoticity of its phase space trajectory

Wave propagation in a strongly disordered 1D phononic lattice supporting rotational waves

We investigate the dynamical properties of a strongly disordered micropolar lattice made up of cubic block units. This phononic lattice model supports both transverse and rotational degrees of freedom hence its disordered variant posses an interesting problem as it can be used to model physically important systems like beam-like microstructures. Different kinds of single site excitations (momentum or displacement) on the two degrees of freedom are found to lead to different energy transport both superdiffusive and subdiffusive. We show that the energy spreading is facilitated both by the low frequency extended waves and a set of high frequency modes located at the edge of the upper branch of the periodic case for any initial condition. However, the second moment of the energy distribution strongly depends on the initial condition and it is slower than the underlying one dimensional harmonic lattice (with one degree of freedom). Finally, a limiting case of the micropolar lattice is studied where Anderson localization is found to persist and no energy spreading takes place

A very brief introduction to quantum computing and quantum information theory for mathematicians

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs of most statements can be found in standard references

High-Resolution NIR Observations of the Circumstellar Disk System in the Bok Globule CB 26

We report on results of near-infrared and optical observations of the mm disk embedded in the Bok globule CB 26 (Launhardt & Sargent 2001). The near-infrared images show a bipolar reflection nebula with a central extinction lane which coincides with the mm disk. Imaging polarimetry of this object yielded a polarization pattern which is typical for a young stellar object surrounded by a large circumstellar disk and an envelope, seen almost edge-on. The strong linear polarization in the bipolar lobes is caused by single scattering at dust grains and allowed to locate the illuminating source which coincides with the center of the mm disk. The spectral energy distribution of the YSO embedded in CB 26 resembles that of a ClassI source with a luminosity of 0.5 L_sun.Using the pre-main-sequence evolutionary tracks and the stellar mass inferred from the rotation curve of the disk, we derive an age of the system of <10^6 yr. H_alpha and [SII] narrow-band imaging as well as optical spectroscopy revealed an Herbig-Haro object 6.15 arcmin northwest of CB 26 YSO 1, perfectly aligned with the symmetry axis of the bipolar nebula. This Herbig-Haro object (HH 494) indicates ongoing accretion and outflow activity in CB 26 YSO 1. Its excitation characteristics indicate that the Herbig-Haro flow is propagating into a low-density environment. We suggest that CB 26 YSO 1 represents the transition stage between embedded protostellar accretion disks and more evolved protoplanetary disks around T Tauri stars in an undisturbed environment.Comment: 21 pages, 6 figures (reduced resolution), ApJ accepte

A boundary integral equation method in the frequency domain for cracks under transient loading

Acknowledgments The financial support of the German Academic Exchange Service (DAAD), Engineering and Physical Sciences Research Council (EPSRC) and Advanced Research Collaboration (ARC) Programme (funded by the British Council and DAAD) is gratefully acknowledged.Peer reviewedPublisher PD

Decoupling of the general scalar field mode and the solution space for Bianchi type I and V cosmologies coupled to perfect fluid sources

The scalar field degree of freedom in Einstein's plus Matter field equations is decoupled for Bianchi type I and V general cosmological models. The source, apart from the minimally coupled scalar field with arbitrary potential V(Phi), is provided by a perfect fluid obeying a general equation of state p =p(rho). The resulting ODE is, by an appropriate choice of final time gauge affiliated to the scalar field, reduced to 1st order, and then the system is completely integrated for arbitrary choices of the potential and the equation of state.Comment: latex2e source file,14 pages, no figures; (v3): minor corrections, to appear in J. Math. Phy

The optimal P3M algorithm for computing electrostatic energies in periodic systems

We optimize Hockney and Eastwood's Particle-Particle Particle-Mesh (P3M) algorithm to achieve maximal accuracy in the electrostatic energies (instead of forces) in 3D periodic charged systems. To this end we construct an optimal influence function that minimizes the RMS errors in the energies. As a by-product we derive a new real-space cut-off correction term, give a transparent derivation of the systematic errors in terms of Madelung energies, and provide an accurate analytical estimate for the RMS error of the energies. This error estimate is a useful indicator of the accuracy of the computed energies, and allows an easy and precise determination of the optimal values of the various parameters in the algorithm (Ewald splitting parameter, mesh size and charge assignment order).Comment: 31 pages, 3 figure

Reduction of Guided Acoustic Wave Brillouin Scattering in Photonic Crystal Fibers

Guided Acoustic Wave Brillouin Scattering (GAWBS) generates phase and polarization noise of light propagating in glass fibers. This excess noise affects the performance of various experiments operating at the quantum noise limit. We experimentally demonstrate the reduction of GAWBS noise in a photonic crystal fiber in a broad frequency range using cavity sound dynamics. We compare the noise spectrum to the one of a standard fiber and observe a 10-fold noise reduction in the frequency range up to 200 MHz. Based on our measurement results as well as on numerical simulations we establish a model for the reduction of GAWBS noise in photonic crystal fibers.Comment: 4 pages, 7 figures; added numerical simulations, added reference

On the universality of small scale turbulence

The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of stochastic Markovian processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more precise method our results call in question the concept of universality.Comment: 4 pages, 4 figure