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报告题目: On the Maxwell-Bloch system in the sharp-line limit without solitons
报 告 人: 李思泰 副教授
报告人所在单位: 厦门大学
报告日期: 2022-12-06
报告时间: 09:00-10:00
报告地点: 腾讯会议 ID: 698-236-507
   
报告摘要:

We study the Cauchy problem for the Maxwell-Bloch equations (MBEs) of light-matter interaction via asymptotics, under assumptions that prevent the generation of solitons. Our analysis clarifies some features in which physically-motivated initial/boundary conditions are satisfied, including: (i) A boundary layer phenomenon is fully explained in which, even for smooth initial data, the solution makes a sudden transition over an infinitesimal propagation distance. At a formal level, this phenomenon has been described by other authors in terms of a self-similar solution related to the Painleve-III (PIII) transcendents. We make this observation precise and also identify this self-similar solution appearing exactly as the leading-order terms in the asymptotics. We show that such PIII functions are identical to the ones discovered recently to play an important role in several limiting processes involving the focusing nonlinear Schrodinger equation. (ii) Our analysis of the asymptotic behavior of solutions reveals slow decay of the electric field in one direction that is actually inconsistent with the simplest version of scattering theory. (iii) The asymptotic results validate a previous proposed causality requirement for MBEs, and demonstrate that it is a build-in mechanism of the Riemann-Hilbert problem studied in this work. (iv) Finally, the spontaneous decay process of an initially unstable medium is proved via a large family of incident optical pulses. This is join work with Peter D. Miller.

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本年度学院报告总序号: 698

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