[geometry-ml:03553] 応用特異点ラボ・シンポジウムのお知らせ。

[izumiya ＠ math.sci.hokudai.ac.jp]

幾何学分科会関係者の皆様

応用特異点ラボ・シンポジウムを以下のように開催しますので
お知らせします。
12月10日のみのミニ研究集会です。

泉屋
	**** Program ***** Title: Mini Workshop on WKB Analysis and Singularity Theory Date: 12/10 @ Science Building, 3-205 10:00 - 10:30, Hiroshi Teramoto (Hokkaido University) Welcome Remarks Abstract : Non-adiabatic transitions play important roles in chemical reaction dynamics. In this mini-workshop, we invite Professor George Hagedorn who are a pioneer of mathematical WKB analysis of non-adiabatic transitions along with two experts of WKB analysis, Professor Akira Shudo and Professor Takuya Watanabe. WKB analysis is deeply related to singularity theory and the aim of this mini workshop is to deepen the relation even further for mutual developments. In this short remark, I will present some motivating examples and our ongoing works. 10:30 - 11:30, George Hagedorn (Virginia Polytechnic Institute and State University) Theory and Numerics for Semiclassical Quantum Mechanics Abstract : We present numerical algorithms for solving the Schr"odinger equation based on semiclassical wave packets. 13:00 - 14:00, Akira Shudo (Tokyo Metropolitan University) TBA 14:30 - 15:00, Takuya Watanabe (Ritsumeikan University) Two-level transition problem for avoided crossings in a non-adiabatic regime Abstract : We study a two-level adiabatic transition probability for a finite number of avoided crossings with a small interaction through a first order 2 x 2 system. The asymptotic behavior of the transition probability when two parameters (an adiabatic parameter $h$ and an energy-gap parameter $varepsilon$) tend to 0 depends on the ratio $h/varepsilon^2$. The exponential decaying property in an adiabatic regime ($h/varepsilon^2 to 0$) has been studied by many researchers and also in a critical regime ($h/varepsilon^2$ is ${mathcal O}(1)$) had been obtained by G.-A. Hagedorn in 1991. In this talk, we give the asymptotic behavior of the transition probability in the other regime ($varepsilon^2/h to 0$) called "non-adiabatic'' regime. In this regime, an exact WKB method can not be adapted because of the confluence of turning points. We would like to report to overcome the difficulty by means of a microlocal analysis in stead of an exact WKB method. This is the joint work with M. Zerzeri (Paris Nord). ******************

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