Let wildlife live: A Computer illustrated calendar of endangered species

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Fluctuations and Ergodicity of the Form Factor of Quantum Propagators and Random Unitary Matrices

We consider the spectral form factor of random unitary matrices as well as of Floquet matrices of kicked tops. For a typical matrix the time dependence of the form factor looks erratic; only after a local time average over a suitably large time window does a systematic time dependence become manifest. For matrices drawn from the circular unitary ensemble we prove ergodicity: In the limits of large matrix dimension and large time window the local time average has vanishingly small ensemble fluctuations and may be identified with the ensemble average. By numerically diagonalizing Floquet matrices of kicked tops with a globally chaotic classical limit we find the same ergodicity. As a byproduct we find that the traces of random matrices from the circular ensembles behave very much like independent Gaussian random numbers. Again, Floquet matrices of chaotic tops share that universal behavior. It becomes clear that the form factor of chaotic dynamical systems can be fully faithful to random-matrix theory, not only in its locally time-averaged systematic time dependence but also in its fluctuations.Comment: 12 pages, RevTEX, 4 figures in eps forma

Nonlinear oscillations of gas bubbles submerged in water: implications for plasma breakdown

Gas bubbles submerged in a dielectric liquid and driven by an electric field can undergo dramatic changes in both shape and volume. In certain cases, this deformation can enhance the distribution of the applied field inside the bubble as well as decrease the internal gas pressure. Both effects will tend to facilitate plasma formation in the gas volume. A practical realization of these two effects could have a broad impact on the viability of liquid plasma technologies, which tend to suffer from high voltage requirements. In this experiment, bubbles of diameter 0.4–0.7 mm are suspended in the node of a 26.4 kHz underwater acoustic standing wave and excited into nonlinear shape oscillations using ac electric fields with amplitudes of 5–15 kV cm −1 . Oscillations of the deformed bubble are photographed with a high-speed camera operating at 5130 frames s −1 and the resulting images are decomposed into their axisymmetric spherical harmonic modes, ##IMG## [http://ej.iop.org/images/0022-3727/45/41/415203/jphysd431220ieqn001.gif] {$Y_l^0$ , using an edge detection algorithm. Overall, the bubble motion is dominated by the first three even modes l = 0, 2 and 4. Electrostatic simulations of the deformed bubble's internal electric field indicate that the applied field is enhanced by as much as a factor of 2.3 above the nominal applied field. Further simulation of both the pure l = 2 and l = 4 modes predicts that with additional deformation, the field enhancement factors could reach as much as 10–50.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98592/1/0022-3727_45_41_415203.pd

Role of electron-electron and electron-phonon interaction effect in the optical conductivity of VO2

We have investigated the charge dynamics of VO2 by optical reflectivity measurements. Optical conductivity clearly shows a metal-insulator transition. In the metallic phase, a broad Drude-like structure is observed. On the other hand, in the insulating phase, a broad peak structure around 1.3 eV is observed. It is found that this broad structure observed in the insulating phase shows a temperature dependence. We attribute this to the electron-phonon interaction as in the photoemission spectra.Comment: 6 pages, 8 figures, accepted for publication in Phys. Rev.

Nonlinear statistics of quantum transport in chaotic cavities

Copyright © 2008 The American Physical Society.In the framework of the random matrix approach, we apply the theory of Selberg’s integral to problems of quantum transport in chaotic cavities. All the moments of transmission eigenvalues are calculated analytically up to the fourth order. As a result, we derive exact explicit expressions for the skewness and kurtosis of the conductance and transmitted charge as well as for the variance of the shot-noise power in chaotic cavities. The obtained results are generally valid at arbitrary numbers of propagating channels in the two attached leads. In the particular limit of large (and equal) channel numbers, the shot-noise variance attends the universal value 1∕64β that determines a universal Gaussian statistics of shot-noise fluctuations in this case.DFG and BRIEF

How often is a random quantum state k-entangled?

The set of trace preserving, positive maps acting on density matrices of size d forms a convex body. We investigate its nested subsets consisting of k-positive maps, where k=2,...,d. Working with the measure induced by the Hilbert-Schmidt distance we derive asymptotically tight bounds for the volumes of these sets. Our results strongly suggest that the inner set of (k+1)-positive maps forms a small fraction of the outer set of k-positive maps. These results are related to analogous bounds for the relative volume of the sets of k-entangled states describing a bipartite d X d system.Comment: 19 pages in latex, 1 figure include

Seasonal Dynamics of Lipid Metabolism and Energy Storage in the Brazilian Free-Tailed Bat

As small, flying, mammalian endotherms, insectivorous bats are adapted to operate at high levels of energy expenditure. In response to seasonally variable challenges, we predicted that bats should balance energy budgets by flexibly adjusting aspects of their physiology or behavior in ways that elevate metabolic capacity. We examined variation in energy storage and pathways for oxidative metabolism in Brazilian free-tailed bats (Tadarida brasiliensis) related to estimated costs associated with reproduction and migration. We collected pectoral muscle and liver from female T. brasiliensis at six time points during the summer and fall and measured changes in the activity of four enzymes involved with lipid metabolism. Body mass varied substantially with life-cycle stage, suggesting that rapid accumulation and use of fat stores occurs in response to current and anticipated energy demands. Catabolic enzyme activity (carnitine palmitoyltransferase [CPT], 3-hydroxyacyl-CoA dehydrogenase [HOAD], and citrate synthase [CS]) in the muscle was increased during lactation compared with early pregnancy but exhibited no change before fall migration. While there was no temporal change in lipid biosynthetic capacity in the liver, fatty acid synthase activity was negatively correlated with body mass. Variation in body mass and enzyme activity in T. brasiliensis during the summer suggests that stored energy is mobilized and lipid oxidative capacity is increased during periods of increased demand and that lipid biosynthetic capacity is increased with depletion of fat stores. These results suggest that bats are able to flexibly adjust metabolic capacity based on energy requirement to maintain energy balance despite high levels of expenditure

Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry

The statistical properties of quantum transport through a chaotic cavity are encoded in the traces \T={\rm Tr}(tt^\dag)^n, where $t$ is the transmission matrix. Within the Random Matrix Theory approach, these traces are random variables whose probability distribution depends on the symmetries of the system. For the case of broken time-reversal symmetry, we present explicit closed expressions for the average value and for the variance of \T for all $n$. In particular, this provides the charge cumulants \Q of all orders. We also compute the moments $$ of the conductance $g=\mathcal{T}_1$. All the results obtained are exact, {\it i.e.} they are valid for arbitrary numbers of open channels.Comment: 5 pages, 4 figures. v2-minor change

Plasma Ignition in Underwater Gas Bubbles.

The ignition of plasma in underwater gas bubbles is a promising method of injecting chemically reactive species into liquids for applications in environmental remediation. To date, these studies have been limited to bubbles attached to the surface of the electrode. This dissertation proposes that plasma can be ignited in bubbles that are separated from the electrode by first deforming the shape of the bubble's dielectric boundary. This approach exploits a phenomenon termed the shape effect, in which the distortion of the dielectric boundary distorts and enhances the applied electric field in the volume of the bubble. The purpose of this dissertation was two-fold: (1) to demonstrate the shape effect by exciting strong deformations in underwater bubbles, and (2) investigate the fundamental mechanisms responsible for plasma formation in isolated bubbles. To accomplish this goal, an experimental apparatus was developed, capable of confining the bubble, deforming the shape of the bubble, and igniting plasma within the bubble interior. The apparatus utilizes ultrasonic acoustic standing waves to trap the bubble at a fixed position underwater and apply electric fields using electrodes that are mounted on a 3D translation stage. In general, it was observed that electric fields in the range 10-25 kV/cm were capable of exciting bubbles into a wide variety of nonlinear deformations, including resonant capillary waves on the bubble surface, spherical harmonic perturbations, and in some cases the complete breakup of the bubble into multiple fragments. Simulations of the electric field in these deformed bubbles indicate that the enhancement of the applied field could be as large as a factor of 10-50. A thorough investigation of fundamental discharge mechanisms in bubble filled liquids was also undertaken. It was shown that in a specific range of voltage and electrode geometry, a new type of streamer is observed that travels through the both liquid and the bubble gas. Under careful adjustment of the operating conditions, the plasma could actually be confined to the bubble when driven by a 12 kV pulse. It was further observed that this isolated bubble plasma could be ignited much easier using a repetitively pulsed voltage source.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99808/1/bsso_1.pd

Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance

Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first part of the paper we attempt to expose systematically ideas underlying the so-called stochastic (Heidelberg) approach to chaotic quantum scattering. Then we concentrate on systems with broken time-reversal invariance coupled to continua via M open channels. By using the supersymmetry method we derive: (i) an explicit expression for the density of S-matrix poles (resonances) in the complex energy plane (ii) an explicit expression for the parametric correlation function of densities of eigenphases of the S-matrix. We use it to find the distribution of derivatives of these eigenphases with respect to the energy ("partial delay times" ) as well as with respect to an arbitrary external parameter.Comment: 51 pages, RevTEX , three figures are available on request. To be published in the special issue of the Journal of Mathematical Physic