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)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys. Rev. E 77, 021128 (2008)], 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 ${\hslash }^2$ 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.

• Received 12 August 2019
• Revised 3 November 2019

DOI:https://doi.org/10.1103/PhysRevE.100.062119