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arXiv 0910.4459quant-ph
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大原子和量子点的基态能量

Ground state energy of large atoms and quantum dots

Hervé Kunz, Rico Rueedi

摘要:

我们确定了电子数N较大的原子和量子点的基态能量。我们表明,占主导地位的条款的能量是由半经典的Hartree-Fock理论。原子的关联效应出现在N ln N阶,量子点的关联效应出现在N阶。我们计算它们。半经典的Hartree-Fock理论在基态能量中产生振荡作为N的函数。这些振荡反映了经典粒子在有费米子势的情况下运动的动力学。原子和一些点的动力学是规则的,但我们提出了一个点的情况下,这种动力学是完全混乱的,我们计算在这种情况下的基态能量的振荡部分。

英文摘要:

We determine the ground state energy of atoms and quantum dots whose number N of electrons is large. We show that the dominant terms of the energy are those given by a semiclassical Hartree-Fock theory. Correlation effects appear at the order N ln N for atoms and the order N for quantum dots. We compute them. The semiclassical Hartree-Fock theory creates oscillations in the ground state energy as a function of N . These oscillations reflect the dynamics of a classical particle moving in the presence of the Thomas-Fermi potential. The dynamics is regular for atoms and some dots, but we present the case of a dot where this dynamics is fully chaotic and we compute the oscillating part of the ground state energy in this case.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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