Fast forward problem for adiabatic quantum dynamics: estimation of the energy cost

We consider the problem of energy cost needed for acceleration (deceleration) of the evolution of a quantum system using the Masuda–Nakamura’s fast forward protocol. In particular, we focus on dynamics by considering models for a quantum box with a moving wall and harmonic oscillator with time-dependent frequency. For both models we computed the energy needed for acceleration (deceleration) as a function of time. The results obtained are compared with those of other acceleration (deceleration) protocols.