薛定谔方程的量子复兴与分形

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2024-04-01 DOI:10.1016/S0034-4877(24)00022-3

Gunwoo Cho, Jimyeong Kim, Ihyeok Seo, Seongyeon Kim, Yehyun Kwon

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引用次数: 0

摘要

我们研究了薛定谔方程在电势影响下的行为，重点是它与量子复兴和分形的关系。我们的研究结果表明，解在非理性时间表现出分形行为，而在理性时间则表现出与初始数据类似的规律性。这将 Oskolkov [16] 和 Rodnianski [18] 关于自由薛定谔演化的结果扩展到了关于势的一般情况。

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QUANTUM REVIVALS AND FRACTALITY FOR THE SCHRÖDINGER EQUATION

We investigate the behavior of the Schrödinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that the solution displays fractal behavior at irrational times, while exhibiting regularity similar to the initial data at rational times. These extend the results of Oskolkov [16] and Rodnianski [18] on the free Schrödinger evolution to the general case regarding potentials.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.