Coelho Stanley S, Queiroz Lucas, Alves Danilo T
Faculdade de Física, Universidade Federal do Pará, Belém 66075-110, PA, Brazil.
Centro de Física, Universidade do Minho, 4710-057 Braga, Portugal.
Entropy (Basel). 2022 Dec 19;24(12):1851. doi: 10.3390/e24121851.
Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency ω0, which undergoes a sudden jump to a frequency ω1 and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis−Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when ω1<ω0. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state.
在过去几十年中，多位作者对频率存在多次突变的谐振子进行了研究。我们研究了一个初始频率为ω0的量子谐振子的动力学，它会突然跃变到频率ω1，并且在经过一定时间间隔后，又突然回到其初始频率。利用动力学不变量的刘易斯 - 里森费尔德方法，我们给出了平均能量值、平均激发数和跃迁概率的表达式，其中考虑了不同于基态的初始状态。我们表明，即使ω1<ω0，振子在跃迁后的平均能量也等于或大于跃迁前的平均能量。我们还表明，对于跃迁之间时间间隔的特定值，振子会回到相同的初始状态。
