磁场中壳模型的零质量约束动力学与统计
Mass-Zero constrained dynamics and statistics for the shell model in magnetic field
摘要：
在物理学的几个领域中，包括第一原理模拟和可极化系统的经典模型，必须执行相对于一组辅助变量的能量函数的最小化以定义物理自由度的动态。在本文中，我们讨论了最近提出的算法，有效地和严格地模拟这种类型的系统：质量零（MaZe）约束动力学。在MaZe中，最小条件作为对辅助变量的约束被施加，辅助变量被视为由物理系统驱动的零惯性的自由度。该方法是制定在拉格朗日框架，使该方法的属性自然出现从一个完全一致的动力学和统计的观点。我们首先介绍MaZe典型的最小化问题，其中所施加的约束是完整的，并总结其关键的正式属性，特别是精确的玻恩-奥本海默动力学其次是物理变量和相应的物理概率密度的精确采样。然后，我们推广的方法的情况下的辅助变量，线性涉及他们的速度的条件。这种情况发生时，例如，当描述系统在外部磁场，他们需要适应MaZe集成半完整约束。本文的第二部分介绍了新的发展，并说明通过一个简单的经典极化模型的NaCl的电荷输运性质的原理证明计算。
英文摘要：
In several domains of physics, including first principle simulations and classical models for polarizable systems, the minimization of an energy function with respect to a set of auxiliary variables must be performed to define the dynamics of physical degrees of freedom. In this paper, we discuss a recent algorithm proposed to efficiently and rigorously simulate this type of systems: the Mass-Zero (MaZe) Constrained Dynamics. In MaZe the minimum condition is imposed as a constraint on the auxiliary variables treated as degrees of freedom of zero inertia driven by the physical system. The method is formulated in the Lagrangian framework, enabling the properties of the approach to emerge naturally from a fully consistent dynamical and statistical viewpoint. We begin by presenting MaZe for typical minimization problems where the imposed constraints are holonomic and summarizing its key formal properties, notably the exact Born-Oppenheimer dynamics followed by the physical variables and the exact sampling of the corresponding physical probability density. We then generalize the approach to the case of conditions on the auxiliary variables that linearly involve their velocities. Such conditions occur, for example, when describing systems in external magnetic field and they require to adapt MaZe to integrate semiholonomic constraints. The new development is presented in the second part of this paper and illustrated via a proof-of-principle calculation of the charge transport properties of a simple classical polarizable model of NaCl.
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