Robust maximization of asymptotic growth

This paper addresses the question of how to invest in a robust growth-optimal way in a market where the instantaneous expected return of the underlying process is unknown. The optimal investment strategy is identified using a generalized version of the principal eigenfunction for an elliptic second-order differential operator, which depends on the covariance structure of the underlying process used for investing. The robust growth-optimal strategy can also be seen as a limit, as the terminal date goes to infinity, of optimal arbitrages in the terminology of Fernholz and Karatzas [Ann. Appl. Probab. 20 (2010) 1179-1204].Comment: Published in at http://dx.doi.org/10.1214/11-AAP802 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Controlling and observing nonseparability of phonons created in time-dependent 1D atomic Bose condensates

We study the spectrum and entanglement of phonons produced by temporal changes in homogeneous one-dimensional atomic condensates. To characterize the experimentally accessible changes, we first consider the dynamics of the condensate when varying the radial trapping frequency, separately studying two regimes: an adiabatic one and an oscillatory one. Working in momentum space, we then show that in situ measurements of the density-density correlation function can be used to assess the nonseparability of the phonon state after such changes. We also study time-of-flight (TOF) measurements, paying particular attention to the role played by the adiabaticity of opening the trap on the nonseparability of the final state of atoms. In both cases, we emphasize that commuting measurements can suffice to assess nonseparability. Some recent observations are analyzed, and we make proposals for future experiments.Comment: 26 pages, 17 figure

Scattering of gravity waves in subcritical flows over an obstacle

We numerically study the scattering coefficients of linear water waves on stationary flows above a localized obstacle. We compare the scattering on trans- and subcritical flows, and then focus on the latter which have been used in recent analog gravity experiments. The main difference concerns the magnitude of the mode amplification: whereas transcritical flows display a large amplification (which is generally in good agreement with the Hawking prediction), this effect is heavily suppressed in subcritical flows. This is due to the transmission across the obstacle for frequencies less than some critical value. As a result, subcritical flows display high- and low-frequency behaviors separated by a narrow band around the critical frequency. In the low-frequency regime, transmission of long wavelengths is accompanied by non-adiabatic scattering into short wavelengths, whose spectrum is approximately linear in frequency. By contrast, in the high-frequency regime, no simple description seems to exist. In particular, for obstacles similar to those recently used, we observe that the upstream slope still affects the scattering on the downstream side because of some residual transmission.Comment: 21 pages, 17 figure