Abstract: Chambers' expression for the current density in a normal metal in which the electric field varies over a mean free path is derived from a quantum approach in which use is made of the density matrix in the presence of scattering centers but in the absence of the field. An approximate expression used for the latter is shown to reduce to one derived by Kohn and Luttinger for the case of weak scattering. A general space-and time-varying electromagnetic interaction is treated by first-order perturbation theory. The method is applied to superconductors, and a general expression derived for the kernel of the Pippard integral for fields of arbitrary frequency. The expressions derived can also be used to discuss absorption of electromagnetic radiation in thin superconducting films.

Abstract: An investigation of gain and noise bandwidth of phonon-cooled hot-electron bolometric (HEB) mixers is presented. The radiation coupling to the mixers is quasioptical through either a spiral or twin-slot antenna. A maximum gain bandwidth of 4.8 GHz is obtained for mixers based on a 3.5 nm thin NbN film with Tc= 10 K. The noise bandwidth is 5.6 GHz, at the moment limited by parasitic elements in the, device mount fixture. At 0.65 THz the DSB receiver noise temperature is 700-800 К in the IF band 1-2 GHz, and 1150-2700 К in the band 3.5-7 GHz.

Abstract: Aims. We aim to study the physical conditions, particularly the excitation state, of the intermediate-temperature gas components in the protoplanetary nebula CRL 618. These components are particularly important for understanding the evolution of the nebula.
Methods. We performed Herschel/HIFI observations of several CO lines in the far-infrared/sub-mm in the protoplanetary nebula CRL 618. The high spectral resolution provided by HIFI allows measurement of the line profiles. Since the dynamics and structure of the nebula is well known from mm-wave interferometric maps, it is possible to identify the contributions of the different nebular components (fast bipolar outflows, double shells, compact slow shell) to the line profiles. The observation of these relatively high-energy transitions allows an accurate study of the excitation conditions in these components, particularly in the warm ones, which cannot be properly studied from the low-energy lines.
Results. The 12CO J = 16–15, 10–9, and 6–5 lines are easily detected in this source. Both 13CO J = 10–9 and 6–5 are also detected. Wide profiles showing spectacular line wings have been found, particularly in 12CO J = 16–15. Other lines observed simultaneously with CO are also shown. Our analysis of the CO high-J transitions, when compared with the existing models, confirms the very low expansion velocity of the central, dense component, which probably indicates that the shells ejected during the last AGB phases were driven by radiation pressure under a regime of maximum transfer of momentum. No contribution of the diffuse halo found from mm-wave data is identified in our spectra, because of its low temperature. We find that the fast bipolar outflow is quite hot, much hotter than previously estimated; for instance, gas flowing at 100 km s-1 must have a temperature higher than ~200 K. Probably, this very fast outflow, with a kinematic age <100 yr, has been accelerated by a shock and has not yet cooled down. The double empty shell found from mm-wave mapping must also be relatively hot, in agreement with the previous estimate.