Integrable Anisotropic Evolution Equations on a Sphere

V.V. Sokolov's modifying symmetry approach is applied to anisotropic evolution equations of the third order on the n-dimensional sphere. The main result is a complete classification of such equations. Auto-B\"acklund transformations are also found for all equations.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Automatic facial expression tracking for 4D range scans

This paper presents a fully automatic approach of spatio-temporal facial expression tracking for 4D range scans without any manual interventions (such as specifying landmarks). The approach consists of three steps: rigid registration, facial model reconstruction, and facial expression tracking. A Scaling Iterative Closest Points (SICP) algorithm is introduced to compute the optimal rigid registration between a template facial model and a range scan with consideration of the scale problem. A deformable model, physically based on thin shells, is proposed to faithfully reconstruct the facial surface and texture from that range data. And then the reconstructed facial model is used to track facial expressions presented in a sequence of range scans by the deformable model

Numerical calculations of diffraction losses in advanced interferometric gravitational wave detectors

Knowledge of the diffraction losses in higher-order modes of large optical cavities is essential for predicting three-mode parametric photon-phonon scattering, which can lead to mechanical instabilities in long-baseline gravitational wave detectors. We explore different numerical methods in order to determine the diffraction losses of the higher-order optical modes. Diffraction losses not only affect the power buildup inside the cavity but also influence the shape and frequency of the mode, which ultimately affect the parametric instability gain. Results depend on both the optical mode shape (order) and the mirror diameter. We also present a physical interpretation of these results

Effects of spin imbalance on the electric-field driven quantum dissipationless spin current in pp-doped Semiconductors

It was proposed recently by Murakami et al. [Science \textbf{301}, 1348(2003)] that in a large class of $p$-doped semiconductors, an applied electric field can drive a quantum dissipationless spin current in the direction perpendicular to the electric field. In this paper we investigate the effects of spin imbalance on this intrinsic $spin$ Hall effect. We show that in a real sample with boundaries, due to the presence of spin imbalance near the edges of the sample, the spin Hall conductivity is not a constant but a sensitively $position$-$dependent$ quantity, and due to this fact, in order to take the effects of spin imbalance properly into account, a microscopic calculation of both the quantum dissipationless spin Hall current and the spin accumulation on an equal footing is thus required. Based on such a microscopic calculation, a detailed discussion of the effects of spin imbalance on the intrinsic spin Hall effect in thin slabs of $p$-doped semiconductors are presented.Comment: 8 pages, 2 figures, An extended version with detailed calculations To appear in Phys. Rev.

Quantum ground-state cooling and tripartite entanglement with three-mode optoacoustic interactions

We present a quantum analysis of three-mode optoacoustic parametric interactions in an optical cavity, in which two orthogonal transverse optical-cavity modes are coupled to one acoustic mode through radiation pressure. Due to the optimal frequency matching -- the frequency separation of two cavity modes is equal to the acoustic-mode frequency -- the carrier and sideband fields simultaneously resonate and coherently build up. This mechanism significantly enhances the optoacoustic couplings in the quantum regime. It allows exploration of quantum behavior of optoacoustic interactions in small-scale table-top experiments. We show explicitly that given an experimentally achievable parameter, three-mode scheme can realize quantum ground-state cooling of milligram scale mechanical oscillators and create robust stationary tripartite optoacoustic quantum entanglements.Comment: 20 pages, 5 figure

The Algebraic Structure of the gl(n∣m)gl(n|m) Color Calogero-Sutherland Models

We extend the study on the algebraic structure of the $su(n)$ color Calogero-Sutherland models to the case of $gl(n|m)$ color CS model and show that the generators of the super-Yangian $Y(gl(n|m))$ can be obtained from two $gl(n|m)$ loop algebras. Also, a super $W_{\infty}$ algebra for the SUSY CS model is constructed.Comment: LaTeX, 13 page