The thermodynamic equilibrium in a system of randomly quantized vortices in superfluid helium with counterflow between the normal and superfluid components is considered. Both continuum and discrete approaches are studied. Even when using the continuum approach for the system as a whole, the partition function for the various vortex loop configurations can only be calculated by involving the discrete approach. It is obvious that discretization is important to numerical studies. Numerical simulation is the main tool for solving the stochastic dynamics of quantum vortex filaments subject to random force, due to their complexity. Some physical consequences of the results are discussed.

中文翻译：

---

量化涡旋的随机动力学：连续和离散方法

考虑了超流氦中随机量子化涡旋系统中的热力学平衡，其中正常和超流成分之间存在逆流。研究了连续和离散方法。即使对整个系统使用连续体方法，也只能通过涉及离散方法来计算各种涡环配置的配分函数。显然，离散化对数值研究很重要。由于其复杂性，数值模拟是求解受随机力作用的量子涡旋细丝随机动力学的主要工具。讨论了结果的一些物理后果。