具有部分周期边界条件系统的Yukawa势I：准二维系统的Ewald和
Yukawa potentials in systems with partial periodic boundary conditions I : Ewald sums for quasi-two dimensional systems
摘要：
汤川势常被用作胶体、等离子体等系统的有效势。当德拜屏蔽长度较大时，汤川势趋向于非屏蔽库仑势;在这个小屏蔽极限或库仑极限下，势是长程的。众所周知，在计算机模拟中，简单的长程势截断和最小镜像约定不足以获得系统的精确数值数据。体系统的Ewald方法，即在空间的所有三个方向上具有周期性边界条件，已经推导出了Yukawa势[cf.是的，Rosenfeld，{ \it Mol. Phys.}，\bm{88}，1357，（1996）和G.，Salin和J. - M.，Caillol，{ \it J. Chem. Phys.}，\bm{113}，10459，（2000）]，但是对于具有部分周期边界条件的系统，Ewald和只是最近才被获得[M.，Mazars，{ \it J. Chem. Phys.}，{ \bf 126}，056101（2007）]。本文给出了具有任意德拜长度且仅在两个方向上具有周期边界条件的系统中Yukawa势的Ewald和的封闭导子。特别注意库仑极限及其与系统电中性的关系。
英文摘要：
Yukawa potentials are often used as effective potentials for systems as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential ; in this small screening limit, or Coulomb limit, the potential is long ranged. As it is well known in computer simulation, a simple truncation of the long ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of the space, has already been derived for Yukawa potential [cf. Y., Rosenfeld, {\it Mol. Phys.}, \bm{88}, 1357, (1996) and G., Salin and J.-M., Caillol, {\it J. Chem. Phys.}, \bm{113}, 10459, (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [M., Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. A special attention is paid to the Coulomb limit and its relation with the electroneutrality of systems.
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