强磁场中原子的一维模型，II：朗道能级的反对称性
One-dimensional models for atoms in strong magnetic fields, II: Anti-Symmetry in the Landau Levels
摘要：
强磁场中的电子可以用一维模型来描述，其中库仑势和相互作用被与最低朗道带相关的正则化所取代。对于这些类型的一个大类的模型，我们表明，可以绑定的电子的最大数量是小于Z + Zf（Z）。函数f（Z）表示当磁场强度随核电荷Z的多项式增长时，在log Z中为二次的小的非线性增长。与以前的工作相比，这里考虑的模型包括那些产生于现实的情况下，其中的N-电子的完整审判波函数是产品的N-电子审判功能在一维和反对称产品的状态在最低的朗道水平。
英文摘要：
Electrons in strong magnetic fields can be described by one-dimensional models in which the Coulomb potential and interactions are replaced by regularizations associated with the lowest Landau band. For a large class of models of these type, we show that the maximum number of electrons that can be bound is less than a Z + Z f(Z). The function f(Z) represents a small non-linear growth which is quadratic in log Z when the magnetic field strength grows polynomially with the nuclear charge Z. In contrast to earlier work, the models considered here include those arising from realistic cases in which the full trial wave function for N-electrons is the product of an N-electron trial function in one-dimension and an antisymmetric product of states in the lowest Landau level.
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