An Experimental Proposal to Test Dynamic Quantum Non-locality with Single-Atom Interferometry

Quantum non-locality based on the well-known Bell inequality is of kinematic nature. A different type of quantum non-locality, the non-locality of the quantum equation of motion, is recently put forward with connection to the Aharonov-Bohm effect [Nature Phys. 6, 151 (2010)]. Evolution of the displacement operator provides an example to manifest such dynamic quantum non-locality. We propose an experiment using single-atom interferometry to test such dynamic quantum non-locality. We show how to measure evolution of the displacement operator with clod atoms in a spin-dependent optical lattice potential and discuss signature to identify dynamic quantum non-locality under a realistic experimental setting.Comment: 4 page

Emergent conformal symmetry for black holes without Z2\mathbb{Z}_2 symmetry

We investigate the motion of the massless scalar field and the nearly bound null geodesic in the near-ring region of a black hole with either acceleration or Misner charge, around which the photon ring deviates from the equatorial plane. In the eikonal limit, we demonstrate that the massless scalar field exhibits an emergent $\mathfrak{s l}(2, \mathbb{R})_{\mathrm{QN}}$ conformal algebra in the near-ring region. Additionally, in the nearly bound limit, we observe the emergence of an $\mathfrak{s l}(2, \mathbb{R})_{\mathrm{PR}}$ conformal algebra for the null geodesics that form the photon ring in the black hole image. Our findings indicate that the emergent $\mathfrak{s l}(2, \mathbb{R})$ conformal symmetry persists even for black holes without $\mathbb{Z}_2$ symmetry, thus expanding the foundations of photon ring holography.Comment: 21 page

DFR: Depth from Rotation by Uncalibrated Image Rectification with Latitudinal Motion Assumption

Despite the increasing prevalence of rotating-style capture (e.g., surveillance cameras), conventional stereo rectification techniques frequently fail due to the rotation-dominant motion and small baseline between views. In this paper, we tackle the challenge of performing stereo rectification for uncalibrated rotating cameras. To that end, we propose Depth-from-Rotation (DfR), a novel image rectification solution that analytically rectifies two images with two-point correspondences and serves for further depth estimation. Specifically, we model the motion of a rotating camera as the camera rotates on a sphere with fixed latitude. The camera's optical axis lies perpendicular to the sphere's surface. We call this latitudinal motion assumption. Then we derive a 2-point analytical solver from directly computing the rectified transformations on the two images. We also present a self-adaptive strategy to reduce the geometric distortion after rectification. Extensive synthetic and real data experiments demonstrate that the proposed method outperforms existing works in effectiveness and efficiency by a significant margin

Solving second kind integral equations by Galerkin methods with continuous orthogonal wavelets

AbstractIn this paper, We use the continuous wavelets on the interval constructed by Cohen et al. (Appl. Comput. Harm. Anal. 1 (1993) 54–81) to solve the second kind integral equations. To this end, we give the decomposition and reconstruction algorithm for these wavelets, and construct the quadrature formulae for the calculation of inner products of any functions and the scaling functions, which are required in the wavelet-Galerkin methods for integral equations. In this method, the integral kernels are represented in these wavelet bases as sparse matrices, to high precision. Thus, we present an efficient algorithm for numerical solution of second kind integral equations

Numerical Simulation Analysis of Water Injection Seepage Law in Micro Porous Structure of Coal

In this paper, a nano Voxel X-ray 3D microscope is used to scan the long flame coal samples and to reconstruct the 3D pore structure by the use of microscopic computed tomography. With image segmentation technique, a model of micro-pore structure of coal is obtained from the reconstructed coal. With different planes selected as seepage inlets, a numerical simulation of low-pressure water seepage is conducted. Studies show that water pressure gradually decreases along the direction of water seepage and reaches the maximum at the pore-pipes with good connectivity near the inlet. Due to the difference between the structure and development direction of pores in the three dimensions, there is an optimal seepage outlet that is most appropriately corresponding to each seepage inlet. When different planes are selected as seepage inlets, the velocity of each seepage outlet is positively correlated with the seepage mass flow rate at the outlet