Analysis of methods for calculating the static characteristics of dense Coulomb systems
Keywords:
one-component plasma, Coulomb system, hyper-netted chain approximation, Ornstein-Zernike integral equation, Cauchy-Schwarz inequality.Abstract
In this paper, various methods for calculating static characteristics of plasma, such as HNC, MHNC, VMHNC, Percus-Yevik and analytical models were analyzed to satisfy a mathematical condition.
Structural characteristics of a one-component plasma were reconstructed in a wide range of coupling parameters within the most requested various modern methods (HNC, MHNC, VMHNC, Percus-Yevik, and analytical models). All these methods were analyzed to fulfill the fundamental Cauchy – Schwartz mathematical inequality. As a result a HNC method with the empirical expression of the bridge function and one of the recent methods for obtaining a structural factor based on a parameterized formula does not satisfy the inequality. The other methods for calculating static characteristics listed above beside the stated ones satisfy the condition. For the general analysis of a method, functional dependence was obtained expressing the Cauchy-Schwartz inequality. This dependence includes the frequency moments, which are defined within the framework of the method of moments. To satisfy the inequality, this relationship must be strictly positive. For each considered method of obtaining static structural characteristics, this relationship was calculated and analyzed. As a result, it was found that a number of methods do not satisfy the Cauchy-Schwartz inequality.
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