Condensed Matter

    

Zeta-Pad'e SRWS Theory with Approximation of Averaged Summation

Authors: Yoshiki Ueoka

In my previous paper about Statistical Random Walk Summation(SRWS) theory[1], I proposed a new expansion of typical critical Green function for the Anderson transition in the Orthogonal class. In this paper, I perform an approximate summation for the series of the typical critical Green function. Pad'e approximant is used to take a summation. The new approximate expression of the critical exponent nu of localization length is obtained. The dimensional dependence of the critical exponent is directly related with Riemann zeta function. Thus, the number theory and the critical phenomena of the Anderson transition is connected. Therefore I call this method as zeta-Pad'e SRWS theory. Existence of lower critical dimension is understood as the infinite existence of prime numbers. Besides it, analogy with statistical mechanics also becomes clear.

Comments: 7 Pages. High dimensional approximation used in previous version becomes not necessary.

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Submission history

[v1] 2022-05-29 21:59:56
[v2] 2022-06-27 02:00:55
[v3] 2022-09-02 08:23:46

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