强磁场中金属电导率角图的复杂性类
The complexity classes of angular diagrams of the metal conductivity in strong magnetic fields
摘要：
我们考虑描述在相当强的磁场中金属的磁导率对磁场方向的依赖性的角图。如图所示，所有的角电导率图都可以分为有限数量的具有不同复杂性的类。在这些图中，最令人感兴趣的是具有最大复杂性的图，这可能发生在具有相当复杂的费米表面的金属上。在描述复杂图的结构时，除了对电导率本身的描述外，对不同方向的磁场的霍尔电导率的描述起着非常重要的作用。为了评估金属导电率角图的复杂性，将这种图与为整个色散关系定义的完整数学图（形式上）进行比较也是方便的。
英文摘要：
We consider angular diagrams describing the dependence of the magnetic conductivity of metals on the direction of the magnetic field in rather strong fields. As it can be shown, all angular conductivity diagrams can be divided into a finite number of classes with different complexity. The greatest interest among such diagrams is represented by diagrams with the maximal complexity, which can occur for metals with rather complicated Fermi surfaces. In describing the structure of complex diagrams, in addition to the description of the conductivity itself, the description of the Hall conductivity for different directions of the magnetic field plays very important role. For the evaluation of the complexity of angular diagrams of the conductivity of metals, it is convenient also to compare such diagrams with the full mathematical diagrams that are defined (formally) for the entire dispersion relation.
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