Researcher Database

（Last updated : 2024-05-07 12:12:46）　

FUJIIE Setsuro

Department / Course College of Science and Engineering Department of Mathematical Sciences

Title / Position Professor

Other Affiliations
1.	Graduate School of Science and Engineering

Academic background
1.		Doctoral Program (2nd Semester) │ Mathematics Major │ Graduate School, Division of Natural Science │ Kyoto University │ Unfinished
2.	1994/11 Degree Acquisition	│ Tohoku University Ph.D. (Science)
3.	1989/03 Degree Acquisition	│ Kyoto University master degree
4.	～1989/03	Doctoral Program (1st Semester) │ Graduate School, Division of Natural Science │ Kyoto University │ Completed

Research activities
1.		Mthematical Society of Japan

Subject of research
1.	Asymptotic distribution of resonances
2.	Global behavior of WKB solutions
3.	Spectrum of non-selfadjoint operators

Research summary
Semi-Classical Analysis of Schroedinger Equations Semi-classical analysis is an asymptotic analysis where the Planck constant appearing in the Schrödinger equation is regarded as small parameter. It is expected that the quantum mechanics approaches in some sense the classical mechanics in the semi-classical limit (Bohr's correspondence principle). The asymptotic distribution of eigenvalues or resonances created by a bound or semi-bound state respectively is closely related to the existence and the geometry of "trapped" trajectories of the corresponding classical dynamics. This problem is an extension of the famous question “Can one hear the shape of the drum?” (M.Kac), which asks the relation between the geometry of a bounded domain.and the asymptotic distribution of eigenvalues of its Dirichlet Laplacian. The useful WKB method consists in constructing globally an asymptotic power series solution with respect to the Planck constant. The point is that this power series diverges and that the asymptotic form changes discontinuously when passing through turning points or caustics. This so-called Stokes phenomenon is a key to solve the above problem.

Present specialized field
Basic Analysis, General Mathematics (includes Probability Theory/Statistical Mathematics), Mathematical physics/ Fundamental condensed matter physics (Keyword：Schroedinger Equation, Quantum Mechanics, Semi-classical Analysis, Microlocal Analysis, WKB Analysis, Asymptotic Analysis Partial Differential Equations, Ordinary Differential Equations)

Books
1.	2018	Resonances for homoclinic trapped sets │ 405 (Co-authored)
2.	2014/02	Nonlinear Physical Systems Chapter 2 WKB Solutions Near an Unstable Equilibrium and Applications │ ,pp.15-39 (Co-authored)

Papers
1.	2023	Semiclassical WKB problem for the non-self-adjoint Dirac operator with an analytic rapidly oscillating potential │ J. Differ. Equations. │ 360,pp.90-150 (Co-authored)
2.	2020/01	Semiclassical WKB problem for the non-self-adjoint Dirac operator with analytic potential │ Journal of Mathematical Physics │ 61 (1) (Co-authored)
3.	2019	Barrier-top resonances for non globally analytic potentials │ Journal of Spectral Theory │ 9 (1),pp.315 - 348 (Co-authored)
4.	2018	Quantization condition for multi-barrier resonances │ RIMS Kokyuroku Bessatsu │ B67,pp.43-54 (Co-authored)
5.	2018	Quantization conditions of eigenvalues for semiclassical Zakharov-Shabat systems on the circle │ Discrete and Continuous Dynamical Systems │ 38 (3),pp.3851-3873 (Co-authored)
Display All（27）

Academic conference presentation
1.	2024/01/19	Energy-level crossing of a matrix Schrödinger operator and semiclassical resonances 1,2 (Analyse Spectrale pour des Hamiltoniens Quantiques)
2.	2022/12/16	Some quantum effects by crossings of classical trajectories in matrix Schrödinger operators (愛媛大学解析セミナー)
3.	2022/03/18	WKB and microlocal approach to various Bohr-Sommerfeld quantization rules (Geometric Structure and Differential Equations)
4.	2020/01/09	Eigenvalues and resonances created by energy-level crossings (Schroedinger Operators and Related Topics)
5.	2019/12/20	Double well problem for a system of Schroedinger operators
Display All（44）

Other research achievements
1.	2019/06/11 ～ 2019/06/13	Quantum Resonances and Related Topics (Institut Poincare (Paris))
2.	2019/03/04 ～ 2019/03/06	Himeji Conference on Partial Differential Equations
3.	2015/12/14 ～ 2015/12/18	国際研究集会"Semiclassical Analysis and Non-Self-Adjoint Operators"組織委員　（フランス　マルセイユ　CIRM）
4.	2013/02/22 ～ 2013/02/23	国際研究集会"Himeji Conference on Partial Differential Equations"開催 (Egret Himeji)
5.	2011/02/19 ～ 2011/02/20	国際研究集会"Himeji Conference on Partial Differential Equations"開催 (Egret Himeji)
Display All（11）

Teaching achievements

●Other Special Instructions about Teaching Activities

1.	2010/10	Organizer of the school on semiclassical analysis by french lecturers: "Lectures on Semi-Classical Analysis