The excitation of a quantum gas of independent fermions in a deforming cavity: periodicity of driving vs. Landau-Zener transitions

The numerically calculated excitation of a quantum gas of 112 non-interacting fermions in a hard-walled cavity changing its shape is analysed for one and for half of the oscillation cycle. Spheroidal and Legendre polynomial distortions, P₂, P₃, P₄, P₅ and P₆, around the sphere and the octupole deformed shape are considered. Oscillations of the excitation energy as a function of the driving frequency, especially pronounced for low frequencies, are related to quantum interference between Landau-Zener transitions at successively traversed avoided crossings. This irregular component of excitation may be linked to the periodicity of the driving motion since it is strongly suppressed for one-half of the oscillation period. It is argued that the wall formula describes quantum one-body dissipation in aperiodic processes better than in periodic ones.