Dynamics of Quantum Vortex in Superfluid and Superconductor

本研究的目的是研究超流和超导体中涡旋的动力学及其统计规律。我们数值积分的3-D时间相关的Gross-Pitaevskii方程，以研究如何超流湍流状态动态变化从初始条件完全复杂。通过改变系统尺度从256^3到2048^3，对超流湍流的能谱进行了数值研究。我们证实了Kolmogorov的5/3定律在系统中是成立的，并且系统的惯性范围随着系统尺寸的变化而变宽。然而，我们发现量子化涡旋的瓶颈效应阻碍了能量级联从大尺度到小尺度的平滑转换。能谱中出现一个凸点图形。我们还发现，量子化涡旋的纠缠态使大尺度自相似结构类似于经典湍流。

Aim of this research is to study dynamics of vortex and its statistical law in superfluid and superconductor. We numerically integrate the 3-D time-dependent Gross-Pitaevskii equation in order to examine how superfluid turbulent state dynamically changes from initial conditions fully complicated. The energy spectrum of the superfluid turbulence is studied numerically by change the system size from 256^3 to 2048^3. We confirm that the Kolmogorov's 5/3 low is valid in the system and the inertial range become wide with changing the system size. However, we find that the bottleneck effect of quantized vortex prevent the smooth energy cascade transferring from large scale to small one. A bump figure appears in the energy spectrum. We also find that the tangle state of quantized vortex make large scale self-similarity structure like a classical turbulence.