61,762 research outputs found

    Geometric phases and anholonomy for a class of chaotic classical systems

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    Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures

    Quantum Spectra of Triangular Billiards on the Sphere

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    We study the quantal energy spectrum of triangular billiards on a spherical surface. Group theory yields analytical results for tiling billiards while the generic case is treated numerically. We find that the statistical properties of the spectra do not follow the standard random matrix results and their peculiar behaviour can be related to the corresponding classical phase space structure.Comment: 18 pages, 5 eps figure

    Runway grooving project at Chicago Midway Airport

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    Runway grooving project at Chicago Midway Airpor

    Statistical Properties of Many Particle Eigenfunctions

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    Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions appear which reflect the emergence of the canonical ensemble as the number of particles approaches infinity. This arises through a little known asymptotic limit of Bessel functions. Constraints due to symmetries, boundaries, and collisions between particles can be included.Comment: 13 pages, 4 figure

    Note on the helicity decomposition of spin and orbital optical currents

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    In the helicity representation, the Poynting vector (current) for a monochromatic optical field, when calculated using either the electric or the magnetic field, separates into right-handed and left-handed contributions, with no cross-helicity contributions. Cross-helicity terms do appear in the orbital and spin contributions to the current. But when the electric and magnetic formulas are averaged ('electric-magnetic democracy'), these terms cancel, restoring the separation into right-handed and left-handed currents for orbital and spin separately.Comment: 10 pages, no figure

    Garment Construction

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    PDF pages: 4

    The past is the future: innovative designs in acute stroke therapy trials

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    A Developmental Model of Congenital Nystagmus

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    Purpose: Congenital nystagmus (CN) is a spontaneous oscillation of the eyes with an onset in the first few months of life. In 90% of affected children there is an associated underlying sensory defect (foveal hypoplasia, cone dysfunction, cataracts, etc.). In 10% no underlying visual defect can be found, and the nystagmus is labelled as ‘idiopathic’. CN appears to be a developmental anomaly of sensorimotor integration, as it is not have an onset later in infancy or beyond, but why such a wide variety of early onset visual defects should lead to life-long oscillation of the eyes is a mystery. Previous models have focussed on a systems level approach to explain how CN might be generated by known oculomotor circuits. We ask, instead, why CN might occur. Model: Our basic tenet is that infant visuomotor development is highly plastic during some early ‘critical’ period. A defect of foveal vision occurring during (and only during) this period leads to an anomalous connectivity in the oculomotor circuitry, which becomes permanent thereafter. We propose that circuitry normally used for precise foveal registration of a visual object (gaze holding, fixation, and smooth pursuit) develops to maintain some degree of image motion, as this would maximise contrast for a low spatial frequency system. However, this motion is in conflict with maintaining the image on the fovea (or its remnant). We explore the best oculomotor strategy to cope with this conflict. Results: The optimal strategy (in the least squares sense) is to oscillate the eyes in one meridian with alternating slow and quick (saccade) phases. Remarkably, the optimal waveform profile has an increasing-velocity profile. Many of the unique waveforms seen empirically in CN are also optimal strategies given realistic uncertainty in the initial position of a slow phase. Using non-linear dynamical systems analysis, we show that these ‘optimal’ oscillations have similar fractional correlation dimensions to observed data. We also show that a ‘null region’, as commonly observed in CN, would be an inevitable consequence of a velocity driven oculomotor system. Conclusions: We have developed a new approach to understanding oculomotor development, in which we examine the best strategy to maximise visual contrast. In a normal foveate visual system with fine oculomotor control, the best strategy is to develop good foveal registration, which we call ‘fixation’, and ‘smooth pursuit’. If, however, the fovea is absent or not being stimulated (eg. cataracts), the best strategy would be to develop oscillations of the type seen in CN. It implies that the chaotic oscillations are the result of a physiological developmental adaptive process. This is in contrast to the prevailing view that CN is a disease that can be ‘cured’. It is not surprising that CN has proven remarkably refractory to therapeutic intervention with only minimal (if any) long-term successes using drugs, surgery, or even biofeedback. We argue that CN is as adaptive and permanent as normal eye movements are in a normally sighted individual
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