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

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

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.

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 periodsof 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.