Analytical result on the supercurrent through a superconductor/quantum-dot/superconductor junction

We present an analytical result for the supercurrent across a superconductor/quantum-dot/superconductor junction. By converting the current integration into a special contour integral, we can express the current as a sum of the residues of poles. These poles are real and give a natural definition of the Andreev bound states. We also use the exact result to explain some features of the supercurrent transport behavior.Comment: 8 pages, 2 figure

Resolving Scale Ambiguity Via XSlit Aspect Ratio Analysis

In perspective cameras, images of a frontal-parallel 3D object preserve its aspect ratio invariant to its depth. Such an invariance is useful in photography but is unique to perspective projection. In this paper, we show that alternative non-perspective cameras such as the crossed-slit or XSlit cameras exhibit a different depth-dependent aspect ratio (DDAR) property that can be used to 3D recovery. We first conduct a comprehensive analysis to characterize DDAR, infer object depth from its AR, and model recoverable depth range, sensitivity, and error. We show that repeated shape patterns in real Manhattan World scenes can be used for 3D reconstruction using a single XSlit image. We also extend our analysis to model slopes of lines. Specifically, parallel 3D lines exhibit depth-dependent slopes (DDS) on their images which can also be used to infer their depths. We validate our analyses using real XSlit cameras, XSlit panoramas, and catadioptric mirrors. Experiments show that DDAR and DDS provide important depth cues and enable effective single-image scene reconstruction