Importance sampling in Diffusion Monte Carlo has a long history. However, only recently, simulations of ground state properties have been extended to spaces mapped with non-Cartesian coordinates. We demonstrate that in spaces with nonzero advection the Smoluchowski operator for any nontrivial trial wavefunction does not converge to the exact result. Rather, every drift term is equivalent to some advection in a manifold that contains the physical space of the system. Since these manifolds may be formulated with gradient torsion we demonstrate with several numerical experiments that Diffusion Monte Carlo is possible in these as well.

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关于具有多值映射，边界和梯度扭转的空间中的蒙特卡洛扩散

扩散中的重要性采样蒙特卡洛历史悠久。但是，直到最近，对基态属性的模拟才扩展到使用非笛卡尔坐标映射的空间。我们证明，在具有非零对流的空间中，对于任何非平凡的试验波函数，Smoluchowski算子都不会收敛到精确的结果。相反，每个漂移项都等同于包含系统物理空间的歧管中的某些对流。由于这些歧管可以用梯度扭力来配制，因此我们通过几个数值实验证明了扩散蒙特卡洛法也可行。