Lev B I, Zagorodny A G
Bogolyubov Institute for Theoretical Physics, NAS Ukraine, Metrolohichna Street 14-b, Kyiv 03680, Ukraine.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061115. doi: 10.1103/PhysRevE.84.061115. Epub 2011 Dec 8.
The solution of the problem of the partition function calculation for a Coulomb-like system is proposed. The quantum-field-theory approach is used to give a statistical description of a system of interacting particles with due regard to arbitrary spatially inhomogeneous configurations. Formation of structures in a Coulomb-like system is analyzed and applied to the case of of dusty crystals and two-dimensional colloidal crystals. In the one-dimensional case, an exact solution for the spatial distribution of charged particles is obtained. In the two- dimensional case, the exact partition function for homogeneous distribution of particles is presented. We have analytically derived the necessary condition for the crystal formation in a system of interacting particles in the three-dimensional case.
提出了一种用于计算类库仑系统配分函数问题的解决方案。采用量子场论方法，在充分考虑任意空间非均匀构型的情况下，对相互作用粒子系统进行统计描述。分析了类库仑系统中结构的形成，并将其应用于尘埃晶体和二维胶体晶体的情况。在一维情况下，得到了带电粒子空间分布的精确解。在二维情况下，给出了粒子均匀分布的精确配分函数。我们通过解析推导得出了三维情况下相互作用粒子系统中晶体形成的必要条件。
