Time scale of forerunners in quantum tunneling

The forerunners preceding the main tunneling signal of the wave created by a source with a sharp onset or by a quantum shutter, have been generally associated with over-the-barrier (non-tunneling) components. We demonstrate that, while this association is true for distances which are larger than the penetration lenght, for smaller distances the forerunner is dominated by under-the-barrier components. We find that its characteristic arrival time is inversely proportional to the difference between the barrier energy and the incidence energy, a tunneling time scale different from both the phase time and the B\"uttiker-Landauer (BL) time.Comment: Revtex4, 14 eps figure

Worker heterogeneity, new monopsony, and training

A worker's output depends not only on his/her own ability but also on that of colleagues, who can facilitate the performance of tasks that each individual cannot accomplish on his/her own. We show that this common-sense observation generates monopsony power and is sufficient to explain why employers might expend resources on training employees even when the training is of use to other firms. We show that training will take place in better-than-average or ‘good’ firms enjoying greater monopsony power, whereas ‘bad’ firms will have low-ability workers unlikely to receive much training

Ultra-fast propagation of Schr\"odinger waves in absorbing media

We identify the characteristic times of the evolution of a quantum wave generated by a point source with a sharp onset in an absorbing medium. The "traversal'' or "B\"uttiker-Landauer'' time (which grows linearly with the distance to the source) for the Hermitian, non-absorbing case is substituted by three different characteristic quantities. One of them describes the arrival of a maximum of the density calculated with respect to position, but the maximum with respect to time for a given position becomes independent of the distance to the source and is given by the particle's ``survival time'' in the medium. This later effect, unlike the Hartman effect, occurs for injection frequencies under or above the cut-off, and for arbitrarily large distances. A possible physical realization is proposed by illuminating a two-level atom with a detuned laser

Ray-optical refraction with confocal lenslet arrays

Two parallel lenslet arrays with focal lengths f1 and f2 that share a common focal plane (that is, which are separated by a distance f1+f2) can refract transmitted light rays according to Snell's law, but with the 'sin's replaced with 'tan's. This is the case for a limited range of input angles and other conditions. Such confocal lenslet arrays can therefore simulate the interface between optical media with different refractive indices, n1 and n2, whereby the ratio η=-f2/f1 plays the role of the refractive-index ratio n2/n1. Suitable choices of focal lengths enable positive and negative refraction. In contrast to Snell's law, which leads to nontrivial geometric imaging by a planar refractive-index interface only for the special case of n1=±n2, the modified refraction law leads to geometric imaging by planar confocal lenslet arrays for any value of η. We illustrate some of the properties of confocal lenslet arrays with images rendered using ray-tracing software

Spitzer Observations of Low Luminosity Isolated and Low Surface Brightness Galaxies

We examine the infrared properties of five low surface brightness galaxies (LSBGs) and compare them with related but higher surface brightness galaxies, using Spitzer Space Telescope images and spectra. All the LSBGs are detected in the 3.6 and 4.5um bands, representing the stellar population. All but one are detected at 5.8 and 8.0um, revealing emission from hot dust and aromatic molecules, though many are faint or point-like at these wavelengths. Detections of LSBGs at the far-infrared wavelengths, 24, 70, and 160um, are varied in morphology and brightness, with only two detections at 160um, resulting in highly varied spectral energy distributions. Consistent with previous expectations for these galaxies, we find that detectable dust components exist for only some LSBGs, with the strength of dust emission dependent on the existence of bright star forming regions. However, the far-infrared emission may be relatively weak compared with normal star-forming galaxies.Comment: 20 pages, 8 figures, accepted to Ap

Tunneling dynamics in relativistic and nonrelativistic wave equations

We obtain the solution of a relativistic wave equation and compare it with the solution of the Schroedinger equation for a source with a sharp onset and excitation frequencies below cut-off. A scaling of position and time reduces to a single case all the (below cut-off) nonrelativistic solutions, but no such simplification holds for the relativistic equation, so that qualitatively different ``shallow'' and ``deep'' tunneling regimes may be identified relativistically. The nonrelativistic forerunner at a position beyond the penetration length of the asymptotic stationary wave does not tunnel; nevertheless, it arrives at the traversal (semiclassical or B\"uttiker-Landauer) time "tau". The corresponding relativistic forerunner is more complex: it oscillates due to the interference between two saddle point contributions, and may be characterized by two times for the arrival of the maxima of lower and upper envelops. There is in addition an earlier relativistic forerunner, right after the causal front, which does tunnel. Within the penetration length, tunneling is more robust for the precursors of the relativistic equation