School of Physics, Beihang University, Beijing 100191, China.
Phys Rev E. 2019 Dec;100(6-1):062119. doi: 10.1103/PhysRevE.100.062119.
In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E 75, 050102(R) (2007)PLEEE81539-375510.1103/PhysRevE.75.050102], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys. Rev. E 77, 021128 (2008)PLEEE81539-375510.1103/PhysRevE.77.021128], and coupled harmonic oscillators under driving forces in a simple and unified way. For general quantum systems, a numerical method that approximates the CFs to ℏ^{2} order is proposed. We exemplify the method with a time-dependent frequency harmonic oscillator and a family of quantum systems with time-dependent even power-law potentials.
在相空间中，我们分析得到了受迫谐振子的特征函数（CFs）[Talkner 等人，Phys. Rev. E 75, 050102(R) (2007)PLEEE81539-375510.1103/PhysRevE.75.050102]、时变质量和频率谐振子[Deffner 和 Lutz，Phys. Rev. E 77, 021128 (2008)PLEEE81539-375510.1103/PhysRevE.77.021128]以及受驱动力作用的耦合谐振子，以一种简单统一的方式。对于一般的量子系统，我们提出了一种数值方法，可以将 CFs 近似到ℏ^{2}阶。我们以时变频率谐振子和一族具有时变偶数幂次势能的量子系统为例来说明该方法。
