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微扰随时间指数衰减时谐振子系统能量的单调与非单调增长

  • 李照 ,
  • 杨子倩 ,
  • 张梦男 ,
  • 周晓宇 ,
  • 李永平 ,
  • 刘全慧
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  • 1. 湖南大学物理与微电子科学学院理论物理研究所,湖南长沙410082; 2. 廊坊师范学院物理与电子信息学院,河北廊坊065000
李照( 1993—) ,女,湖南衡阳人,湖南大学理论物理研究所博士生,主要从事量子力学研究工作.

收稿日期: 2016-10-16

  修回日期: 2017-02-13

  网络出版日期: 2017-06-20

基金资助

国家自然科学基金( 11675051) 资助

Monotonic and non-monotonic increase of the energy for a 1D simple harmonic oscillator on action of exponentially-decaying-on-time perturbation

  • LI Zhao ,
  • YANG Zi-qian ,
  • ZHANG Meng-nan ,
  • ZHOU Xiao-yu ,
  • LI Yong-ping ,
  • LIU Quan-hui
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  • 1. College of Physics and Electronics,School for Theoretical Physics,Hunan University,Changsha,Hunan 410082,China; 2. College of Physics and Electronic Information,Langfang Teachers University,Langfang,Hebei 065000,China

Received date: 2016-10-16

  Revised date: 2017-02-13

  Online published: 2017-06-20

Supported by

 

摘要

在含时微扰势能ηxe-t/τ( 其中η 为微扰强度参量,τ 为微扰的特征时间) 作用下,一维谐振子系统能量随时间的变化,可分为单调上升和震荡上升这两种情况.定性来说,可以用微扰特征时间和谐振子的固有频率的比值来区分这两种情况.当这个比值较小,吸收呈现单调上升; 当这个比值较大时,吸收呈现震荡上升.另外,我们还发现,微扰一旦作用,系统就离开基态,短时间内和微扰的特征时间无关.

本文引用格式

李照 , 杨子倩 , 张梦男 , 周晓宇 , 李永平 , 刘全慧 . 微扰随时间指数衰减时谐振子系统能量的单调与非单调增长[J]. 大学物理, 2017 , 36(6) : 9 -14 . DOI: 10.16854 /j.cnki.1000-0712.2017.06.003

Abstract

When a 1D simple harmonic oscillator is under the action of the perturbation that decays exponentially with the increase of time,the energy of the system can increase monotonically or non-monotonically,depends mainly on the ratio of the period of the oscillation and the characteristic time of the perturbation. Once the ratio is small,i.e.,it is much less than 1,the increasing is monotonic; however,which is large,i.e.,it is much greater than 1,the increasing is oscillating with diminishing amplitudes. The physical mechanism is proposed in the following. That the ratio is small means that the perturbation ends practically within one period of the unperturbed system,so the probability of the system in the every energy level cannot change any more. That the ratio is large means that the perturbation needs many periods of the unperturbed system before it ends practically,so the probability of the unperturbed system in the every energy level can change alternatively. Since this physical mechanism holds universally for the perturbation decays on time,the system studied in present paper serves as an illustration. In addition,we have found that once the perturbation acts,the system starts to deviate from the initial state in such a manner that is independent of the characteristic time of the perturbation at very short time of the action.

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