We develop a semi-classical approximation for the scar function in the
Weyl-Wigner representation in the neighborhood of a classically unstable periodic orbit of chaotic two dimensional systems. The prediction of hyperbolic fringes, asymptotic to the stable and unstable manifolds, is verified computationally for a (linear) cat map, after the theory is adapted to a discrete phase space appropriate to a quantized torus. Characteristic fringe patterns can be distinguished even for quasi-energies where the fixed point is not Bohr-quantized. Also the patterns are highly localized in the neighborhood of the periodic orbit and along its stable and unstable manifolds without any long distance patterns that appears for the case of the spectral Wigner function.
Direct Visualization of Relativistic Quantum Scars
University of California, Santa Cruz（加州大学圣克鲁兹分校）；Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Department of Physics, Harvard University（哈佛大学物理系）；Department of Chemistry and Chemical Biology, Harvard University（哈佛大学化学与化学生物学系）；University of Manchester（曼彻斯特大学）；National Graphene Institute, University of Manchester（曼彻斯特大学国家石墨烯研究所）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（日本物质材料研究机构材料纳米构筑研究中心）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（日本物质材料研究机构电子光学材料研究中心）
Classical periodic trajectories and quantum scars in many-spin systems
Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；University of Leipzig（莱比锡大学）
Classical and Quantum Properties of the Spin-Boson Dicke Model: Chaos, Localization, and Scarring
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México（墨西哥国立自治大学应用数学与系统研究所）；CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor（马里博尔大学应用数学与理论物理中心）；Center for Theoretical Physics, Massachusetts Institute of Technology（麻省理工学院理论物理中心）；Department of Physics, University of Connecticut（康涅狄格大学物理系）；Departamento de Física, Cinvestav（墨西哥国家科学技术研究中心物理系）；Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa（墨西哥自治都市大学伊萨帕拉帕校区物理系）；Facultad de Física, Universidad Veracruzana（韦拉克鲁斯大学物理学院）
