Kedia Hridesh, Foster David, Dennis Mark R, Irvine William T M
Department of Physics, James Franck Institute, Enrico Fermi Institute, The University of Chicago, 929 E 57th St., Chicago, Illinois 60637, USA.
HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK.
Phys Rev Lett. 2016 Dec 30;117(27):274501. doi: 10.1103/PhysRevLett.117.274501. Epub 2016 Dec 29.
We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot, and its generalizations. As finite-energy physical fields, they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knotted fields. The construction can be used to generate isolated knotted flux tubes, filled by knots encoded in the lines of the vector field. Lastly, we give examples of manifestly knotted vector fields with vanishing helicity. Our results provide building blocks for analytical models and simulations alike.
我们展示了一种从复标量场构建无散度纽结矢量场的通用方法，其封闭场线编码了多种纽结和链环，包括环面纽结、它们的索结、8字纽结及其推广形式。作为有限能量的物理场，它们代表了诸如等离子体中的磁场或流体中的涡度场等场的初始状态。我们给出了一个从具有纽结零细丝的复标量函数开始计算矢量势的系统程序，从而能够明确计算这些纽结场的螺旋度。该构造可用于生成由矢量场的线中编码的纽结填充的孤立纽结通量管。最后，我们给出了螺旋度为零的明显纽结矢量场的例子。我们的结果为分析模型和模拟提供了构建模块。
