We have combined determinations of the epoch-dependent star formation rate (SFR) function with relationships between SFR and radio (synchrotron and free-free) emission to work out detailed predictions for the counts and the redshift distributions of
star-forming galaxies detected by planned Square Kilometer Array (SKA) surveys. The evolving SFR function comes from recent models fitting the far-infrared (FIR) to millimeter-wave luminosity functions and the ultraviolet (UV) luminosity functions up to z=10, extended to take into account additional UV survey data. We used very deep 1.4 GHz number counts from the literature to check the relationship between SFR and synchrotron emission, and the 95 GHz South Pole Telescope (SPT) counts of dusty galaxies to test the relationship between SFR and free-free emission. We show that the SKA will allow us to investigate the SFRs of galaxies down to few Msun/yr up to z=10, thus extending by more than two orders of magnitude the high-z SFR functions derived from Herschel surveys. SKA1-MID surveys, down to microJy levels, will detect hundreds of strongly lensed galaxies per square degree; a substantial fraction of them will show at least two images above the detection limits.
For a bosonic (fermionic) open system in a bath with many bosons (fermions) modes, we derive the exact non-Markovian master equation in which the memory effect of the bath is reflected in the time dependent decay rates. In this approach, the reduced
density operator is constructed from the formal solution of the corresponding Heisenberg equations. As an application of the exact master equation, we study the active probing of non-Markovianity of the quantum dissipation of a single boson mode of electromagnetic (EM) field in a cavity QED system. The non-Markovianity of the bath of the cavity is explicitly reflected by the atomic decoherence factor.
Motivated by a recent experiment [J. Catani et al., arXiv:1106.0828v1 preprint, 2011], we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical pi
cture of such dynamics at zero temperature, using a time-dependent variational approach. In the Gross-Pitaevskii regime we obtain breathing oscillations whose amplitudes are suppressed by self trapping, due to interactions with the Bose gas. Introducing phonons in the Bose gas leads to the damping of breathing oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results reproduce the main features of the impurity dynamics observed by Catani et al. despite experimental thermal effects, and are supported by simulations of the system in the Gross-Pitaevskii regime. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas.
