Recovering the stationary phase condition for accurately obtaining scattering and tunneling times

The stationary phase method is often employed for computing tunneling {\em phase} times of analytically-continuous {\em gaussian} or infinite-bandwidth step pulses which collide with a potential barrier. The indiscriminate utilization of this method without considering the barrier boundary effects leads to some misconceptions in the interpretation of the phase times. After reexamining the above barrier diffusion problem where we notice the wave packet collision necessarily leads to the possibility of multiple reflected and transmitted wave packets, we study the phase times for tunneling/reflecting particles in a framework where an idea of multiple wave packet decomposition is recovered. To partially overcome the analytical incongruities which rise up when tunneling phase time expressions are obtained, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and a one dimensional squared potential barrier where the scattered wave packets can be recomposed by summing the amplitudes of simultaneously reflected and transmitted waves.Comment: 32 pages, 5 figures, 1 tabl

A Novel Non-invasive Method to Detect RELM Beta Transcript in Gut Barrier Related Changes During a Gastrointestinal Nematode Infection

Currently, methods for monitoring changes of gut barrier integrity and the associated immune response via non-invasive means are limited. Therefore, we aimed to develop a novel non-invasive technique to investigate immunological host responses representing gut barrier changes in response to infection. We identified the mucous layer on feces from mice to be mainly composed of exfoliated intestinal epithelial cells. Expression of RELM-β, a gene prominently expressed in intestinal nematode infections, was used as an indicator of intestinal cellular barrier changes to infection. RELM-β was detected as early as 6 days post-infection (dpi) in exfoliated epithelial cells. Interestingly, RELM-β expression also mirrored the quality of the immune response, with higher amounts being detectable in a secondary infection and in high dose nematode infection in laboratory mice. This technique was also applicable to captured worm-infected wild house mice. We have therefore developed a novel non-invasive method reflecting gut barrier changes associated with alterations in cellular responses to a gastrointestinal nematode infection

Transport and spectroscopic properties of superconductor - ferromagnet - superconductor junctions of La1.9Sr0.1CuO4La_{1.9}Sr_{0.1}CuO_4 - La0.67Ca0.33MnO3La_{0.67}Ca_{0.33}MnO_3 - La1.9Sr0.1CuO4La_{1.9}Sr_{0.1}CuO_4

Transport and Conductance spectra measurements of ramp-type junctions made of cuprate superconducting $La_{1.9}Sr_{0.1}CuO_4$ electrodes and a manganite ferromagnetic $La_{0.67}Ca_{0.33}MnO_3$ barrier are reported. At low temperatures below $T_c$, the conductance spectra show Andreev-like broad peaks superposed on a tunneling-like background, and sometimes also sub-gap Andreev resonances. The energy gap values $\Delta$ found from fits of the data ranged mostly between 7-10 mV. As usual, the gap features were suppressed under magnetic fields but revealed the tunneling-like conductance background. After field cycling to 5 or 6 T and back to 0 T, the conductance spectra were always higher than under zero field cooling, reflecting the negative magnetoresistance of the manganite barrier. A signature of superparamagnetism was found in the conductance spectra of junctions with a 12 nm thick LCMO barrier. Observed critical currents with barrier thickness of 12 nm or more, were shown to be an artifact due to incomplete milling of one of the superconducting electrodes.Comment: 10 figure

Fractional Brownian motion with a reflecting wall

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. While the mean-square displacement of the particle shows the expected anomalous diffusion behavior $\langle x^2 \rangle \sim t^\alpha$, the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case, $\alpha> 1$, the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion, $\alpha < 1$, in contrast, the probability density is depleted close to the barrier. We discuss implications of these findings, in particular for applications that are dominated by rare events.Comment: 6 pages, 6 figures. Final version as publishe

Measuring the temporal coherence of an atom laser beam

We report on the measurement of the temporal coherence of an atom laser beam extracted from a $^{87}$Rb Bose-Einstein condensate. Reflecting the beam from a potential barrier creates a standing matter wave structure. From the contrast of this interference pattern, observed by magnetic resonance imaging, we have deduced an energy width of the atom laser beam which is Fourier limited by the duration of output coupling. This gives an upper limit for temporal phase fluctuations in the Bose-Einstein condensate.Comment: 4 pages, 3 figure

Oscillatory Tunneling between Quantum Hall Systems

Electron tunneling between quantum Hall systems on the same two dimensional plane separated by a narrow barrier is studied. We show that in the limit where inelastic scattering time is much longer than the tunneling time, which can be achieved in practice, electrons can tunnel back and forth through the barrier continously, leading to an oscillating current in the absence of external drives. The oscillatory behavior is dictated by a tunneling gap in the energy spectrum. We shall discuss ways to generate oscillating currents and the phenomenon of natural ``dephasing" between the tunneling currents of edge states. The noise spectra of these junctions are also studied. They contain singularites reflecting the existence of tunneling gaps as well as the inherent oscillation in the system. (Figures will be given upon requests).Comment: 20 pages, OS

Small Corrections to the Tunneling Phase Time Formulation

After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for tunneling/reflecting particles in a particular colliding configuration where the idea of multiple peak decomposition is recovered. To partially overcome the analytical incongruities which frequently rise up when the stationary phase method is adopted for computing the (tunneling) phase time expressions, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and a unidimensional squared potential barrier where the scattered wave packets can be recomposed by summing the amplitudes of simultaneously reflected and transmitted wave components so that the conditions for applying the stationary phase principle are totally recovered. Lessons concerning the use of the stationary phase method are drawn.Comment: 14 pages, 3 figure