发表机构
Sofia University（索非亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导了含时量子蒙特卡洛方法中的条件相互作用，阐明其贝叶斯基础，并推广至旋量情形以处理活跃的交换作用。
AI 中文摘要
含时量子蒙特卡洛方法通过系综的副本集合来表示多电子态，其中每个电子由一个walker云描述，该walker云在物理空间中对其密度进行采样，每个副本对应一个walker和一个引导波函数，并且该方法用基于walker位置构建的条件相互作用替代Hartree势。采样在物理空间而非构型空间中进行，这保证了计算代价的多项式级增长。在此，该条件相互作用是推导得出的而非假设的。该方法迄今主要应用于自旋相反的电子，其中交换作用处于休眠状态而非缺失，而本公式则针对交换作用活跃的情形。将walker视为其电子在有限分辨率下的局域化，贝叶斯定理和单一的经验替换即可得出该方法先前启发式使用的Nadaraya-Watson形式。由此，非局域长度获得了作为条件化宽度的意义，而非拟合耦合参数，并且对相互作用和平均场极限均源自同一构造。对于费米子，交换作用无法由walker承载，而保留在波函数部分，这使得正walker采样免于符号问题。由于条件化消除了在Hartree-Fock中消除正交归一乘子的规范自由度，此处通过由约束推导出的项来强制正交归一性。该公式推广至旋量情形，其中在重合点处的Pauli抑制根据局域自旋排列进行分级，并通过共线极限和平均场极限简化为已知的两粒子自旋方程。
英文摘要
The time-dependent quantum Monte Carlo method represents a many-electron state by an ensemble of replicas, in which each electron is described by a cloud of walkers which samples its density in physical space, one walker and one guide wave per replica, and it replaces the Hartree potential by a conditional interaction built from the walker positions. The sampling is in physical space rather than in configuration space, which is what keeps the cost polynomial. Here that conditional interaction is derived rather than postulated. The method has so far been applied mostly to opposite-spin electrons, where the exchange is dormant rather than absent, and the present formulation addresses the regime in which it is active. Treating the walker as a localization of its electron to a finite resolution, Bayes theorem and a single empirical substitution yield the Nadaraya-Watson form which the method has used heuristically. The nonlocality length thereby acquires a meaning as the width of the conditioning rather than as a fitted coupling, and the pair and mean-field limits follow from one construction. For fermions, exchange cannot be carried by the walkers and stays in the wave sector, which is what leaves the positive walker sampling free of the sign problem. Because the conditioning removes the gauge freedom which eliminates the orthonormality multipliers in Hartree-Fock, orthonormality is enforced here by a term derived from the constraint. The formulation is generalized to spinors, where the Pauli suppression at coincidence becomes graded by the local spin alignment, and it reduces through the collinear and mean-field limits to the known two-particle spin equations.
