Critical scattering in a time-dependent harmonic oscillator

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:492

Article

Ishida, Atsuhide¹  Kawamoto, Masaki² 

[1] Tokyo Univ Sci, Fac Engn, Dept Liberal Arts, Katsushika Ku, 6-3-1 Niijuku, Tokyo 1258585, Japan

[2] Ehime Univ, Grad Sch Sci & Engn, Dept Engn Prod, 3 Bunkyo Cho, Matsuyama, Ehime 7908577, Japan

关键词: Wave operators;    Quantum scattering;    Time-dependent quantum systems;    Harmonic oscillators;   

DOI  :  10.1016/j.jmaa.2020.124475

来源: Elsevier

【 摘 要 】

Controlled time-decaying harmonic oscillator changes the threshold of decay order of the potential functions in order to exist the physical wave operators. This threshold was first reported by Ishida and Kawamoto [6] for the non-critical case. In this paper we deal with the critical case. As for the critical case, the situation changes drastically, and much more rigorous analysis is required than that of non-critical case. We study this critical behavior and clarify the threshold by the power of the log growth of the potential functions. Consequently, this result reveals the asymptotics for quantum dynamics of the critical case. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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