Mughal A, Moore M A
School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 1):011606. doi: 10.1103/PhysRevE.76.011606. Epub 2007 Jul 27.
We study the ground state properties of classical Coulomb charges interacting with a 1/r potential moving on a plane but confined either by a circular hard-wall boundary or by a harmonic potential. The charge density in the continuum limit is determined analytically and is nonuniform. Because of the nonuniform density there are both disclinations and dislocations present and their distribution across the system is calculated and shown to be in agreement with numerical studies of the ground state (or at least low-energy states) of N charges, where values of N up to 5000 have been studied. A consequence of these defects is that although the charges locally form into a triangular lattice structure, the lattice lines acquire a marked curvature. A study is made of conformal crystals to illuminate the origin of this curvature. The scaling of various terms which contribute to the overall energy of the system of charges, viz., the continuum electrostatic energy, correlation energy, surface energy (and so on) as a function of the number of particles N is determined. "Magic number" clusters are those at special values of N whose energies take them below the energy estimated from the scaling forms and are identified with charge arrangements of high symmetry.
我们研究了在平面上运动且受圆形硬壁边界或谐振势约束的、与1/r势相互作用的经典库仑电荷的基态性质。在连续极限下的电荷密度通过解析方法确定，且是非均匀的。由于密度不均匀，存在位错和位错环，计算了它们在整个系统中的分布，并表明其与N个电荷的基态（或至少是低能态）的数值研究结果一致，其中N值高达5000的情况已被研究。这些缺陷的一个结果是，尽管电荷在局部形成三角晶格结构，但晶格线呈现出明显的曲率。对共形晶体进行了研究，以阐明这种曲率的起源。确定了构成电荷系统总能量的各项的标度，即连续静电能、关联能、表面能等作为粒子数N的函数。“幻数”团簇是指在N的特定值处的团簇，其能量低于根据标度形式估计的能量，并与高对称电荷排列相关。
