Adiabatic cycles in quantum systems with contact interactions

An adiabatic cycle involving the $\delta$-function potential is shown to excite Bose particles confined in a one-dimensional box. We consider a cycle, during which a wall described by a $\delta$-potential is applied and its strength and position are slowly varied. When the system is initially prepared in the equilibrium ground state, the adiabatic cycle brings all bosons into the first excited one-particle state, leaving the system in a non-equilibrium state. The absorbed energy during the cycle is proportional to the number of bosons.