arXiv subjects

Hiroaki Kakuma

Publications and source records attributed to Hiroaki Kakuma.

2 recordsLinked to original sources

arXiv2013

Lévy Laplacian for Square Roots of Measures

L.Accardi shows that the Banach space of singed measures is homeomorphic to the Hilbert space formed by so-called root measures. In this paper, we redefine root measures in view of the theory of measures on infinite dimensional spaces, and introduce a notion of differentiation, Fourier transform, and convolution product for root measures, and examine those relations. We also study about Lévy Laplacian on Wiener space as application. It is shown that the symbol of Lévy Laplacian is equal to the quadratic variation of paths.

math.FA↗

arXiv2009

General condition of the Mott transition expressed with the density of state

We have investigated a contribution of the density of state (DOS) to the Mott metal-insulator transition (MIT). The MIT condition is given by the DOS, which usually requires the complicated fundamental equations. To simplify the process, we have derived a general solution of the MIT condition by an integral contains the DOS in the framework of coherent potential approximation. The formula is concise and presents the direct relationship between the MIT condition and the DOS. It is able to calculate the contribution quantitatively and to compare various DOSs analytically.

cond-mat.str-el↗