Mishima Hiroaki, Izumida Yuki
Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Nagoya 464-8601, Japan.
Phys Rev E. 2017 Jul;96(1-1):012133. doi: 10.1103/PhysRevE.96.012133. Epub 2017 Jul 17.
The transitionless tracking (TT) algorithm enables the exact tracking of quantum adiabatic dynamics in an arbitrary short time by adding a counterdiabatic Hamiltonian to the original adiabatic Hamiltonian. By applying Husimi's method originally developed for a quantum parametric oscillator (QPO) to the transitionless QPO achieved using the TT algorithm, we obtain the transition probability generating function with a time-dependent parameter constituted with solutions of the corresponding classical parametric oscillator (CPO). By obtaining the explicit solutions of this CPO using the phase-amplitude method, we find that the time-dependent parameter can be reduced to the frequency ratio between the Hamiltonians without and with the counterdiabatic Hamiltonian, from which we can easily characterize the result achieved by the TT algorithm. We illustrate our theory by showing the trajectories of the CPO on the classical phase space, which elucidate the effect of the counterdiabatic Hamiltonian of the QPO.
无跃迁跟踪（TT）算法通过在原始绝热哈密顿量上添加一个反绝热哈密顿量，能够在任意短时间内精确跟踪量子绝热动力学。通过将最初为量子参数振荡器（QPO）开发的 Husimi 方法应用于使用 TT 算法实现的无跃迁 QPO，我们得到了一个具有随时间变化参数的跃迁概率生成函数，该参数由相应经典参数振荡器（CPO）的解构成。通过使用相幅法获得该 CPO 的显式解，我们发现随时间变化的参数可以简化为有无反绝热哈密顿量时哈密顿量之间的频率比，由此我们可以轻松地刻画 TT 算法所取得的结果。我们通过展示 CPO 在经典相空间上的轨迹来说明我们的理论，这些轨迹阐明了 QPO 的反绝热哈密顿量的作用。
