Semiclassical Description of Tunneling in Mixed Systems: The Case of the Annular Billiard

We study quantum-mechanical tunneling between symmetry-related pairs of regular phase space regions that are separated by a chaotic layer. We consider the annular billiard, and use scattering theory to relate the splitting of quasi-degenerate states quantized on the two regular regions to specific paths connecting them. The tunneling amplitudes involved are given a semiclassical interpretation by extending the billiard boundaries to complex space and generalizing specular reflection to complex rays. We give analytical expressions for the splittings, and show that the dominant contributions come from {\em chaos-assisted}\/ paths that tunnel into and out of the chaotic layer.Comment: 4 pages, uuencoded postscript file, replaces a corrupted versio

Behavioural correlate of choice confidence in a discrete trial paradigm

How animals make choices in a changing and often uncertain environment is a central theme in the behavioural sciences. There is a substantial literature on how animals make choices in various experimental paradigms but less is known about the way they assess a choice after it has been made in terms of the expected outcome. Here, we used a discrete trial paradigm to characterise how the reward history shaped the behaviour on a trial by trial basis. Rats initiated each trial which consisted of a choice between two drinking spouts that differed in their probability of delivering a sucrose solution. Critically, sucrose was delivered after a delay from the first lick at the spouts--this allowed us to characterise the behavioural profile during the window between the time of choice and its outcome. Rats' behaviour converged to optimum choice, both during the acquisition phase and after the reversal of contingencies. We monitored the post-choice behaviour at a temporal precision of 1 millisecond; lick-response profiles revealed that rats spent more time at the spout with the higher reward probability and exhibited a sparser lick pattern. This was the case when we exclusively examined the unrewarded trials, where the outcome was identical. The differential licking profiles preceded the differential choice ratios and could thus predict the changes in choice behaviour.This research was supported by the Australian Research Council Discovery Project Grant DP0987133 to EA

XMM-Newton Spectroscopy of the Starburst Dominated Ultra Luminous Infrared Galaxy NGC 6240

We present new XMM-Newton observation of the Ultra Luminous Infrared Galaxy (ULIRG) NGC 6240. We analyze the reflecting grating spectrometer (RGS) data, and data from the other instruments, and find a starburst dominated 0.5-3 keV spectrum with global properties resembling those observed in M82 but with a much higher luminosity. We show that the starburst region can be divided into an outer zone, beyond a radius of about 2.1 kpc, with a gas temperature of about 10^7 K and a central region with temperatures in the range (2-6) x 10^7 K. The gas in the outer region emits most of the observed Oviii Lyman-alpha line and the gas in the inner region the emission lines of higher ionization ions, including a strong Fexxv line. We also identify a small inner part, very close to the active nuclei, with typical Seyfert 2 properties including a large amount of photoionized gas producing a strong Fe K-alpha 6.4 keV line. The combined abundance, temperature and emission measure analysis indicates super solar Ne/O, Mg/O, Si/O, S/O and possibly also Fe/O. The analysis suggests densities in the range of (0.07-0.28) x epsilon^(-1/2) cm^(-3) and a total thermal gas mass of about 4 x 10^8 x epsilon^(1/2) solar masses, where epsilon is the volume filling factor. We used a simple model to argue that a massive starburst with an age of about 2 x 10^7 years can explain most of the observed properties of the source. NGC 6240 is perhaps the clearest case of an X-ray bright luminous AGN, in a merger, whose soft X-ray spectrum is dominated by a powerful starburst.Comment: 10 pages, 6 diagrams, accepted by ApJ, added a few minor change

Theory of the spontaneous buckling of doped graphene

Graphene is a realization of an esoteric class of materials -- electronic crystalline membranes. We study the interplay between the free electrons and the two-dimensional crystal, and find that it induces a substantial effect on the elastic structure of the membrane. For the hole-doped membrane, in particular, we predict a spontaneous buckling. In addition, attenuation of elastic waves is expected, due to the effect of corrugations on the bulk modulus. These discoveries have a considerable magnitude in graphene, affecting both its mesoscopic structure, and its electrical resistivity, which has an inherent asymmetry between hole- and electron-doped graphene.Comment: Accepted for publication in PR

Computer services for business schools: a procedure for analysis and application to the Sloan School of Management,

Massachusetts Institute of Technology, Alfred P. Sloan School of Management. Thesis. 1974. M.S.MICROFICHE COPY ALSO AVAILABLE IN DEWEY LIBRARY.Bibliography: leaves 83-84.by Doron C. Holzer and Loretta R. Patzelt.M.S