强磁场中的玻色“电子”原子
Atoms with bosonic "electrons" in strong magnetic fields
摘要：
本文研究了在均匀磁场$B$作用下，带核电荷$Z$和$N$玻色子“电子”的原子的基态性质.我们研究了平均场极限$N\to\infty$与$N/Z$固定，并确定了三个不同的渐近区域，根据$B\ll Z^2$，$B\sim Z^2$，和$B\gg Z^2$。在区域1中，标准哈特里理论是适用的。区域3由一维泛函描述，其与由Lieb、Solovej和Yngvason针对区域$B\gg Z^3$中具有费米子电子的原子引入的所谓超强泛函相同;即，对于非常强的磁场，原子的基态性质与统计无关。对于区域2，我们引入了一个一般的{ \it磁Hartree泛函}，这是详细研究。结果表明，在原子的特殊情况下，它可以被限制在零角动量平行于磁场的子空间，这大大简化了理论。的功能再现的能量和一个粒子的约化密度矩阵的完整的$N$粒子基态领先的顺序在$N$，它意味着描述的其他地区的限制情况。
英文摘要：
We study the ground state properties of an atom with nuclear charge $Z$ and $N$ bosonic ``electrons'' in the presence of a homogeneous magnetic field $B$. We investigate the mean field limit $N\to\infty$ with $N/Z$ fixed, and identify three different asymptotic regions, according to $B\ll Z^2$, $B\sim Z^2$, and $B\gg Z^2$. In Region 1 standard Hartree theory is applicable. Region 3 is described by a one-dimensional functional, which is identical to the so-called Hyper-Strong functional introduced by Lieb, Solovej and Yngvason for atoms with fermionic electrons in the region $B\gg Z^3$; i.e., for very strong magnetic fields the ground state properties of atoms are independent of statistics. For Region 2 we introduce a general {\it magnetic Hartree functional}, which is studied in detail. It is shown that in the special case of an atom it can be restricted to the subspace of zero angular momentum parallel to the magnetic field, which simplifies the theory considerably. The functional reproduces the energy and the one-particle reduced density matrix for the full $N$-particle ground state to leading order in $N$, and it implies the description of the other regions as limiting cases.
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