Complete population inversion of Bose particles by an adiabatic cycle

We show that an adiabatic cycle excites Bose particles confined in a one-dimensional box. During the adiabatic cycle, a wall described by a $delta$-shaped potential is applied and its strength and position are slowly varied. When the system is initially prepared in the ground state, namely, in the zero-temperature equilibrium state, the adiabatic cycle brings all bosons into the first excited one-particle state, leaving the system in a nonequilibrium state. The absorbed energy during the cycle is proportional to the number of bosons.