Rigorous derivation of coherent resonant tunneling time and velocity in finite periodic systems

The velocity $v_{res}$ of resonant tunneling electrons in finite periodic structures is analytically calculated in two ways. The first method is based on the fact that a transmission of unity leads to a coincidence of all still competing tunneling time definitions. Thus, having an indisputable resonant tunneling time $\tau_{res},$ we apply the natural definition $v_{res}=L/\tau_{res}$ to calculate the velocity. For the second method we combine Bloch's theorem with the transfer matrix approach to decompose the wave function into two Bloch waves. Then the expectation value of the velocity is calculated. Both different approaches lead to the same result, showing their physical equivalence. The obtained resonant tunneling velocity $v_{res}$ is smaller or equal to the group velocity times the magnitude of the complex transmission amplitude of the unit cell. Only at energies where the unit cell of the periodic structure has a transmission of unity $v_{res}$ equals the group velocity. Numerical calculations for a GaAs/AlGaAs superlattice are performed. For typical parameters the resonant velocity is below one third of the group velocity.Comment: 12 pages, 3 figures, LaTe

Effects of metallicity, star-formation conditions, and evolution in B and Be stars. II: Small Magellanic Cloud, field of NGC 330

We search for effects of metallicity on B and Be stars in the Small and Large Magellanic Clouds (SMC and LMC) and in the Milky Way (MW). We extend our previous analysis of B and Be stars populations in the LMC to the SMC. The rotational velocities of massive stars and the evolutionary status of Be stars are examined with respect to their environments. Spectroscopic observations of hot stars belonging to the young cluster SMC-NGC 330 and its surrounding region have been obtained with the VLT-GIRAFFE facilities in MEDUSA mode. We determine fundamental parameters for B and Be stars with the GIRFIT code, taking into account the effect of fast rotation, and the age of observed clusters. We compare the mean vsini obtained by spectral type- and mass-selection for field and cluster B and Be stars in the SMC with the one in the LMC and MW. We find that (i) B and Be stars rotate faster in the SMC than in the LMC, and in the LMC than in the MW; (ii) at a given metallicity, Be stars begin their main sequence life with a higher initial rotational velocity than B stars. Consequently, only a fraction of B stars that reach the ZAMS with a sufficiently high initial rotational velocity can become Be stars; (iii) the distributions of initial rotational velocities at the ZAMS for Be stars in the SMC, LMC and MW are mass- and metallicity-dependent; (iv) the angular velocities of B and Be stars are higher in the SMC than in the LMC and MW; (v) in the SMC and LMC, massive Be stars appear in the second part of the main sequence, contrary to massive Be stars in the MW

Hawking Radiation on an Ion Ring in the Quantum Regime

This paper discusses a recent proposal for the simulation of acoustic black holes with ions. The ions are rotating on a ring with an inhomogeneous, but stationary velocity profile. Phonons cannot leave a region, in which the ion velocity exceeds the group velocity of the phonons, as light cannot escape from a black hole. The system is described by a discrete field theory with a nonlinear dispersion relation. Hawking radiation is emitted by this acoustic black hole, generating entanglement between the inside and the outside of the black hole. We study schemes to detect the Hawking effect in this setup.Comment: 42 pages (one column), 17 figures, published revised versio

Bloch Approximation in Homogenization and Applications

The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in this paper. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions $u^\varepsilon$ of boundary value problems associated with such operators when the period $\varepsilon>0$ of the coefficients is small. In a previous work by C. Conca and M. Vanninathan [SIAM J. Appl. Math., 57 (1997), pp. 1639--1659], a new proof of weak convergence as $\varepsilon\to 0$ towards the homogenized solution was furnished using Bloch wave decomposition. Following the same approach here, we go further and introduce what we call Bloch approximation, which will provide energy norm approximation for the solution $u^\varepsilon$. We develop several of its main features. As a simple application of this new object, we show that it contains both the first and second order correctors. Necessarily, the Bloch approximation will have to capture the oscillations of the solution in a sharper way. The present approach sheds new light and offers an alternative for viewing classical results

VLTI/MIDI observations of 7 classical Be stars

We measured the mid-infrared extension of the gaseous disk surrounding seven Be stars in order to constrain the geometry of their circumstellar environments and to try to infer physical parameters characterizing these disks. We used the VLTI/MIDI instrument with baselines up to 130 m to obtain an angular resolution of about 15 mas in the N band and compared our results with previous K band measurements obtained with the VLTI/AMBER instrument and/or the CHARA interferometer. We obtained one calibrated visibility measurement for each of the four stars, p Car, zeta Tau, kappa CMa, and alpha Col, two for delta Cen and beta CMi, and three for alpha Ara. Almost all targets remain unresolved even with the largest VLTI baseline of 130m, evidence that their circumstellar disk extension is less than 10 mas. The only exception is alpha Ara, which is clearly resolved and well-fitted by an elliptical envelope with a major axis a=5.8+-0.8mas and an axis ratio a/b=2.4+-1 at 8 microns. This extension is similar to the size and flattening measured with the VLTI/AMBER instrument in the K band at 2 microns. The size of the circumstellar envelopes for these classical Be stars does not seem to vary strongly on the observed wavelength between 8 and 12microns. Moreover, the size and shape of Alpha Ara's disk is almost identical at 2, 8, and 12microns

Entanglement between photons and atoms coupled out from a Bose-Einstein-Condensate

We study the limitations to the relative number squeezing between photons and atoms coupled out from a homogeneous Bose-Einstein-Condensate. We consider the coupling between the translational atomic states by two photon Bragg processes, with one of the photon modes involved in the Bragg process in a coherent state, and the other initially unpopulated. We start with an interacting Bose- condensate at zero temperature and compute the time evolution for the system. We study the squeezing, i.e. the variance of the occupation number difference between the second photon and the atomic c.m. mode. We discuss how collisions between the atoms and photon rescattering affect the degree of squeezing which may be reached in such experiments.Comment: 4 pages RevTeX, 3 figure

Fundamental parameters of Be stars located in the seismology fields of COROT

In preparation for the COROT space mission, we determined the fundamental parameters (spectral type, temperature, gravity, vsini) of the Be stars observable by COROT in its seismology fields (64 Be stars). We applied a careful and detailed modeling of the stellar spectra, taking into account the veiling caused by the envelope, as well as the gravitational darkening and stellar flattening due to rapid rotation. Evolutionary tracks for fast rotators were used to derive stellar masses and ages. The derived parameters will be used to select Be stars as secondary targets (i.e. observed for 5 consecutive months) and short-run targets of the COROT mission. Furthermore, we note that the main part of our stellar sample is falling in the second half of the main sequence life time, and that in most cases the luminosity class of Be stars is inaccurate in characterizing their evolutionary status.Comment: 25 pages, 9 figures, Accepted for publication in A&

Single electron quantum tomography in quantum Hall edge channels

We propose a quantum tomography protocol to measure single electron coherence in quantum Hall edge channels and therefore access for the first time the wave function of single electron excitations propagating in ballistic quantum conductors. Its implementation would open the way to quantitative studies of single electron decoherence and would provide a quantitative tool for analyzing single to few electron sources. We show how this protocol could be implemented using ultrahigh sensitivity noise measurement schemes.Comment: Version 3: long version (7 figures): corrections performed and references have been added. Figures reprocessed for better readabilit