量子库仑系统的热力学极限。部件II。应用
The Thermodynamic Limit of Quantum Coulomb Systems. Part II. Applications
摘要：
在以前的论文中，我们已经发展了一个热力学极限的一般理论。在这里，我们将其应用到三个不同的库仑量子系统，我们证明了每单位体积的自由能的收敛性。第一个系统是晶体，其原子核是在空间中周期性排列的经典粒子，只有电子是量子粒子。我们恢复并推广了February man的一个结果.在第二个例子中，原子核和电子都是量子粒子，受到周期性磁场的作用。从而推广了Lieb和Lebowitz的一个开创性结果。最后，在最后一个例子中，我们再次采用经典核，但优化了它们的位置。据我们所知，这样的系统以前从未被处理过。在前面的论文中介绍的假设的验证使用了几个工具，这些工具在大型量子系统的研究中已经介绍过。特别是，静电不等式的格拉夫和申克是我们的新方法的一个主要成分。
英文摘要：
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the crystal for which the nuclei are classical particles arranged periodically in space and only the electrons are quantum particles. We recover and generalize a previous result of Fefferman. In the second example, both the nuclei and the electrons are quantum particles, submitted to a periodic magnetic field. We thereby extend a seminal result of Lieb and Lebowitz. Finally, in our last example we take again classical nuclei but optimize their position. To our knowledge such a system was never treated before. The verification of the assumptions introduced in the previous paper uses several tools which have been introduced before in the study of large quantum systems. In particular, an electrostatic inequality of Graf and Schenker is one main ingredient of our new approach.
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