arXiv subjects

Yoshiki Ueoka

Publications and source records attributed to Yoshiki Ueoka.

3 recordsLinked to original sources

arXiv2022

$ζ$-Pade SRWS theory with lowest order approximation

In my previous paper about SRWS-$ζ$ theory[Y.Ueoka,viXra:2205.014,2022], I proposed an approximation of rough averaged summation of typical critical Green function for the Anderson transition in the Orthogonal class. In this paper, I remove a rough approximate summation for the series of the typical critical Green function by replacing summation with integral. Pade approximant is used to take a summation. The perturbation series of the critical exponent $ν$ of localization length from upper critical dimension is obtained. The dimensional dependence of the critical exponent is again directly related with Riemann $ζ$ function. Degree of freedom about lower critical exponent improve estimate compared with previous studies. When I fix lower critical dimension equal to two, I obtained similar estimate of the critical exponent compared with fitting curve estimate of the critical exponent[E.Tarquini et al.,PhysRevB.95(2017)094204]. 1

cond-mat.dis-nn↗

arXiv2017

Borel-Padé re-summation of the $β$-functions describing Anderson localisation in the Wigner-Dyson symmetry classes

We describe a Borel-Padé re-summation of the $β$-function in the three Wigner-Dyson symmetry classes. Using this approximate $β$-function we discuss the dimensional dependence of the critical exponent and compare with numerical estimates. We also estimate the lower critical dimension of the symplectic symmetry class.

cond-mat.dis-nn↗

arXiv2014

Dimensional Dependence of Critical Exponent of the Anderson Transition in the Orthogonal Universality Class

We report improved numerical estimates of the critical exponent of the Anderson transition in Anderson's model of localization in $d=4$ and $d=5$ dimensions. We also report a new Borel-Padé analysis of existing $ε$ expansion results that incorporates the asymptotic behaviour for $d\to \infty$ and gives better agreement with available numerical results.

cond-mat.dis-nn↗