Exact ground state energy of a system with an arbitrary number of dipoles at the sites of a regular one-dimensional crystal lattice
Exact ground state energy of a system with an arbitrary number of dipoles at the sites of a regular one-dimensional crystal lattice
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DOI：
10.1016/j.jpcs.2022.111044
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发表时间：
2022-10
影响因子：
4
通讯作者：
O. Ciftja
中科院分区：
文献类型：
--
作者：
O. Ciftja
我们考虑一个有限的经典系统的电偶极子定位在一个规则的一维晶格的网站。它表明，这样的系统的基态能量可以精确计算任意数量的偶极子。对于任意数量的偶极子，基态能量的表达式可以用特殊的函数给出，例如黎曼zeta函数和polygamma函数，并且当偶极子的数量趋于无穷大时，在热力学极限中减少到正确的结果。更简单，但非常准确，基态能量的近似表达式也被引入。
We consider a finite classical system of electric dipoles localized at the sites of a regular one-dimensional crystal lattice. It is shown that the ground state energy of such a system can be calculated exactly for an arbitrary number of dipoles. The expression for the ground state energy can be given in terms of special functions such as Riemann zeta functions and polygamma functions for any arbitrary number of dipoles, and reduces to the correct result in the thermodynamic limit as the number of dipoles tends to infinity. Simpler, but very accurate, approximate expressions for the ground state energy are also introduced.