热力学极限下广义多体系统的Lanczos算法
The Lanczos Algorithm for extensive Many-Body Systems in the Thermodynamic Limit
摘要：
我们严格地建立了Lanczos过程的标度性质，该过程应用于任意的广延多体系统，该系统被进行到收敛n到无穷大，并取热力学极限N到无穷大。在这个限制的解决方案的限制Lanczos系数被发现完全和一般通过两个等价的方程组，给定初始知识的确切累积量生成函数。在此区域中的Lanczos过程的测度和正交多项式系统也明确给出。给出了这些Lanczos函数的一些重要表示，包括Taylor级数展开，并证明了控制它们一般性质的定理。
英文摘要：
We establish rigourously the scaling properties of the Lanczos process applied to an arbitrary extensive Many-Body System which is carried to convergence n to infinity and the thermodynamic limit N to infinity taken. In this limit the solution for the limiting Lanczos coefficients are found exactly and generally through two equivalent sets of equations, given initial knowledge of the exact cumulant generating function. The measure and the Orthogonal Polynomial System associated with the Lanczos process in this regime are also given explicitly. Some important representations of these Lanczos functions are given, including Taylor series expansions, and theorems controlling their general properties are proven.
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