A Compact Fireball Model of Gamma Ray Bursts

It is proposed that the gamma ray burst photons near the peak of the spectrum at several hundred KeV are produced on very compact scales, where photon production is limited by blackbody effects and/or the requirement of energetic quanta ($E>2m_e c^2$) for efficient further production. The fast variation of order milliseconds in the time profile is then a natural expectation, given the other observed GRB parameters. Analytic calculations are presented to show that the escape of non-thermal, energetic gamma rays can emerge within a second of the thermal photons from a gammasphere of below $10^{12}$ cm. The minimum asymptotic bulk Lorentz factor in this model is found to be of order several hundred if the photosphere is of order $3 \times 10^{11}$ cm and greater for larger or smaller photospheric radii. It is suggested that prompt UHE gamma rays might provide a new constraint on the asymptotic Lorentz factor of the outflow.Comment: To appear in ApJ, revisions requested by the refere

The Strong Levinson Theorem for the Dirac Equation

We consider the Dirac equation in one space dimension in the presence of a symmetric potential well. We connect the scattering phase shifts at E=+m and E=-m to the number of states that have left the positive energy continuum or joined the negative energy continuum respectively as the potential is turned on from zero.Comment: Submitted to Physical Review Letter

Scattering by a contact potential in three and lower dimensions

We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising that it gives a nonvanishing cross section when $\alpha=1$ and $\Omega=-1$. When the contact potential is approached by a spherical square well potential instead of the above spherical shell one, one obtains basically the same result except that the parameter $\Omega$ that gives a nonvanishing cross section is different. Similar problems in two and one dimensions are studied and results of the same nature are obtained.Comment: REVTeX, 9 pages, no figur

Extrapolation of K to \pi\pi decay amplitude

We examine the uncertainties involved in the off-mass-shell extrapolation of the $K\rightarrow \pi\pi$ decay amplitude with emphasis on those aspects that have so far been overlooked or ignored. Among them are initial-state interactions, choice of the extrapolated kaon field, and the relation between the asymptotic behavior and the zeros of the decay amplitude. In the inelastic region the phase of the decay amplitude cannot be determined by strong interaction alone and even its asymptotic value cannot be deduced from experiment. More a fundamental issue is intrinsic nonuniqueness of off-shell values of hadronic matrix elements in general. Though we are hampered with complexity of intermediate-energy meson interactions, we attempt to obtain a quantitative idea of the uncertainties due to the inelastic region and find that they can be much larger than more optimistic views portray.Comment: 16 pages with 5 eps figures in REVTE

Quantum dot dephasing by edge states

We calculate the dephasing rate of an electron state in a pinched quantum dot, due to Coulomb interactions between the electron in the dot and electrons in a nearby voltage biased ballistic nanostructure. The dephasing is caused by nonequilibrium time fluctuations of the electron density in the nanostructure, which create random electric fields in the dot. As a result, the electron level in the dot fluctuates in time, and the coherent part of the resonant transmission through the dot is suppressed

Using a neural network approach for muon reconstruction and triggering

The extremely high rate of events that will be produced in the future Large Hadron Collider requires the triggering mechanism to take precise decisions in a few nano-seconds. We present a study which used an artificial neural network triggering algorithm and compared it to the performance of a dedicated electronic muon triggering system. Relatively simple architecture was used to solve a complicated inverse problem. A comparison with a realistic example of the ATLAS first level trigger simulation was in favour of the neural network. A similar architecture trained after the simulation of the electronics first trigger stage showed a further background rejection.Comment: A talk given at ACAT03, KEK, Japan, November 2003. Submitted to Nuclear Instruments and Methods in Physics Research, Section

A Mesoscopic Quantum Eraser

Motivated by a recent experiment by Buks et al. [Nature 391, 871 (1998)] we consider electron transport through an Aharonov-Bohm interferometer with a quantum dot in one of its arms. The quantum dot is coupled to a quantum system with a finite number of states acting as a which-path detector. The Aharonov-Bohm interference is calculated using a two-particle scattering approach for the joint transitions in detector and quantum dot. Tracing over the detector yields dephasing and a reduction of the interference amplitude. We show that the interference can be restored by a suitable measurement on the detector and propose a mesoscopic quantum eraser based on this principle.Comment: 7 pages, 2 figures, to appear in Europhys. Lett., uses EuroPhys.sty and EuroMacro.tex (included

Acoustoelectric effect in a finite-length ballistic quantum channel

The dc current induced by a coherent surface acoustic wave (SAW) of wave vector q in a ballistic channel of length L is calculated. The current contains two contributions, even and odd in q. The even current exists only in a asymmetric channel, when the electron reflection coefficients r_1 and r_2 at both channel ends are different. The direction of the even current does not depend on the direction of the SAW propagation, but is reversed upon interchanging r_1 and r_2. The direction of the odd current is correlated with the direction of the SAW propagation, but is insensitive to the interchange of r_1 and r_2. It is shown that both contributions to the current are non zero only when the electron reflection coefficients at the channel ends are energy dependent. The current exhibits geometric oscillations as function of qL. These oscillations are the hallmark of the coherence of the SAW and are completely washed out when the current is induced by a flux of non-coherent phonons. The results are compared with those obtained previously by different methods and under different assumptions.Comment: 7 pages, 2 figure