Josephson Oscillation and Transition to Self-Trapping for Bose-Einstein-Condensates in a Triple-Well Trap

We investigate the tunnelling dynamics of Bose-Einstein-Condensates(BECs) in a symmetric as well as in a tilted triple-well trap within the framework of mean-field treatment. The eigenenergies as the functions of the zero-point energy difference between the tilted wells show a striking entangled star structure when the atomic interaction is large. We then achieve insight into the oscillation solutions around the corresponding eigenstates and observe several new types of Josephson oscillations. With increasing the atomic interaction, the Josephson-type oscillation is blocked and the self-trapping solution emerges. The condensates are self-trapped either in one well or in two wells but no scaling-law is observed near transition points. In particular, we find that the transition from the Josephson-type oscillation to the self-trapping is accompanied with some irregular regime where tunnelling dynamics is dominated by chaos. The above analysis is facilitated with the help of the Poicar\'{e} section method that visualizes the motions of BECs in a reduced phase plane.Comment: 10 pages, 11 figure

Super Vust theorem and Schur-Sergeev duality for principal finite WW-superalgebras

In this paper, we first formulate a super version of Vust theorem associated with a regular nilpotent element $e\in\mathfrak{gl}(V)$. As an application of this theorem, we then obtain the Schur-Sergeev duality for principal finite $W$-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality.Comment: 35 pages, comments are welcom

PIXOR: Real-time 3D Object Detection from Point Clouds

We address the problem of real-time 3D object detection from point clouds in the context of autonomous driving. Computation speed is critical as detection is a necessary component for safety. Existing approaches are, however, expensive in computation due to high dimensionality of point clouds. We utilize the 3D data more efficiently by representing the scene from the Bird's Eye View (BEV), and propose PIXOR, a proposal-free, single-stage detector that outputs oriented 3D object estimates decoded from pixel-wise neural network predictions. The input representation, network architecture, and model optimization are especially designed to balance high accuracy and real-time efficiency. We validate PIXOR on two datasets: the KITTI BEV object detection benchmark, and a large-scale 3D vehicle detection benchmark. In both datasets we show that the proposed detector surpasses other state-of-the-art methods notably in terms of Average Precision (AP), while still runs at >28 FPS.Comment: Update of CVPR2018 paper: correct timing, fix typos, add acknowledgemen

The Spectral Invariant Approximation within Canopy Radiative Transfer to Support the Use of the EPIC/DSCOVR Oxygen B-band for Monitoring Vegetation

EPIC (Earth Polychromatic Imaging Camera) is a 10-channel spectroradiometer onboard DSCOVR (Deep Space Climate Observatory) spacecraft. In addition to the NIR (780 nm) and the ‘red’ (680 nm) channels, EPIC also has the O2 A-band (764±0.2 nm) and B-band (687.75±0.2 nm). The EPIC at-sensor Normalized Difference Vegetation Index (NDVI) is defined as the difference between NIR and ‘red’ channels normalized to their sum. However, the use of the O2 B-band instead of the ‘red’ channel mitigates the effect ofatmosphere on surface reflectance because it reduces contribution from the radiation scattered by theatmosphere. Applying the radiative transfer theory and the spectral invariant approximation to EPIC observations, we provide supportive arguments for using the O2 band instead of the red channel for monitoring the vegetation dynamics