Moyal Quantization, Holography, and the Quantum Geometry of Surfaces

An elementary introduction is provided to the phase space quantization method of Moyal and Wigner. We generalize the method so that it applies to 2-dimensional surfaces, where it has an interesting connection with quantum holography. In the case of Riemann surfaces the connection between Moyal quantization and holography provides new insights into the Torelli theorem and the quantization of non-linear integrable models. Quantum holography may also serve as a model for a quantum theory of membranes.Comment: PostScript, 15 page

Reply to Comment on "Roughness of Interfacial Crack Fronts: Stress-Weighted Percolation in the Damage Zone"

This is the reply to a Comment by Alava and Zapperi (cond-mat/0401568) on Schmittbuhl, Hansen and Batrouni, PRL, 90, 045505 (2003)

Perfect Anomalous Reflection with a Binary Huygens' Metasurface

In this paper we propose a new metasurface that is able to reflect a known incoming electromagnetic wave into an arbitrary direction, with perfect power efficiency. This seemingly simple task, which we hereafter call perfect anomalous reflection, is actually highly non-trivial due to the differing wave impedances and complex interference between the incident and reflected waves. Heretofore, proposed metasurfaces which achieve perfect anomalous reflection require complicated, deeply subwavelength and/or multilayer element structures which allow them to couple to and from leaky and/or evanescent waves. In contrast, we demonstrate that using a Binary Huygens' Metasurface (BHM) --- a passive and lossless metasurface with only two cells per period --- perfect anomalous reflection can be achieved over a wide angular and frequency range. Through simulations and experiments at 24 GHz, we show that a properly designed BHM can anomalously reflect an incident electromagnetic wave from $\theta_i = 50^\circ$ to $\theta_r = -22.5^\circ$, with perfect power efficiency to within experimental precision

Composition variation and underdamped mechanics near membrane proteins and coats

We study the effect of membrane proteins on the shape, composition and thermodynamic stability of the surrounding membrane. When the coupling between membrane composition and curvature is strong enough the nearby composition and shape both undergo a transition from over-damped to under-damped spatial variation, well before the membrane becomes unstable in the bulk. This transition is associated with a change in the sign of the thermodynamic energy and hence has the unusual features that it can favour the early stages of coat assembly necessary for vesiculation (budding), while suppressing the activity of mechanosensitive membrane channels and transporters. Our results also suggest an approach to obtain physical parameters that are otherwise difficult to measure