Super-expanders and warped cones

For a Banach space $X$, we show that any family of graphs quasi-isometric to levels of a warped cone $\mathcal O_\Gamma Y$ is an expander with respect to $X$ if and only if the induced $\Gamma$-representation on $L^2(Y;X)$ has a spectral gap. This provides examples of graphs that are an expander with respect to all Banach spaces of non-trivial type

How Future Space-Based Weak Lensing Surveys Might Obtain Photometric Redshifts Independently

We study how the addition of on-board optical photometric bands to future space-based weak lensing instruments could affect the photometric redshift estimation of galaxies, and hence improve estimations of the dark energy parameters through weak lensing. Basing our study on the current proposed Euclid configuration and using a mock catalog of galaxy observations, various on-board options are tested and compared with the use of ground-based observations from the Large Synoptic Survey Telescope (LSST) and Pan-STARRS. Comparisons are made through the use of the dark energy Figure of Merit, which provides a quantifiable measure of the change in the quality of the scientific results that can be obtained in each scenario. Effects of systematic offsets between LSST and Euclid photometric calibration are also studied. We find that adding two (U and G) or even one (U) on-board optical band-passes to the space-based infrared instrument greatly improves its photometric redshift performance, bringing it close to the level that would be achieved by combining observations from both space-based and ground-based surveys while freeing the space mission from reliance on external datasets.Comment: Accepted for publication in PASP. A high-quality version of Fig 1 can be found on http://www.ap.smu.ca/~sawicki/DEphoto

Quantitative Determination of the Adiabatic Condition Using Force-Detected Nuclear Magnetic Resonance

The adiabatic condition governing cyclic adiabatic inversion of proton spins in a micron-sized ammonium chloride crystal was studied using room temperature nuclear magnetic resonance force microscopy. A systematic degradation of signal-to-noise was observed as the adiabatic condition became violated. A theory of adiabatic following applicable to cyclic adiabatic inversion is reviewed and implemented to quantitatively determine an adiabaticity threshold $(\gamma H_1)^2/(\omega_{osc}\Omega) = 6.0$ from our experimental results.Comment: 5 pages, 3 fig

Thickness dependence of magnetic properties of (Ga,Mn)As

We report on a monotonic reduction of Curie temperature in dilute ferromagnetic semiconductor (Ga,Mn)As upon a well controlled chemical-etching/oxidizing thinning from 15 nm down to complete removal of the ferro- magnetic response. The effect already starts at the very beginning of the thinning process and is accompanied by the spin reorientation transition of the in-plane uniaxial anisotropy. We postulate that a negative gradient along the growth direction of self-compensating defects (Mn interstitial) and the presence of surface donor traps gives quantitative account on these effects within the p-d mean field Zener model with adequate mod- ifications to take a nonuniform distribution of holes and Mn cations into account. The described here effects are of practical importance for employing thin and ultrathin layers of (Ga,Mn)As or relative compounds in concept spintronics devices, like resonant tunneling devices in particular.Comment: 4 pages, 4 figures and supplementary information 2 pages, 1 figur