Exact WKB analysis of ℂℙ1 holomorphic blocks

On the exact WKB analysis of microdifferential operators of WKB type ∗ Takashi AOKI

QHJ, WKB and exact quantisation

We present a simple derivation of the WKB quantisation condition using the quantum Hamilton-Jacobi formalism and propose an exact quantisation condition within this formalism for integrable models in higher dimensions.

Virtual Turning Points — A gift of microlocal analysis to the exact WKB analysis ?

School of Science and Engineering, Kinki University, Higashi-Osaka 577-8502, Japan Department of Mathematics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502 Japan Hitachi Ltd., Asagaya-kita 2-13-2,...

On global aspects of exact WKB analysis of operators admitting infinitely many phases

A case-study of the Stokes geometry in the large is given for some concrete examples of WKB type operators that admit infinitely many phases. In all the examples discussed in this article virtual turning points and new Stokes curves emanating from them neatly resolve the trouble we encounter. Some computerassisted study of the configuration of the steepest descent paths is employed to show that...

WKB analysis of higher order

WKB analysis of higher order Painlevé equations with a large parameter. II. — Structure theorem for instanton-type solutions of (P J) m (J = I, 34, II-2 or IV) near a simple P-turning point of the first kind