The excitation of an independent-particle gas—classical or quantal—by a time-dependent potential well

A systematic numerical investigation of the excitation of a classical or quantal gas of non-interacting particles in a time-dependent potential well is described. The excitation energy was followed in time for one oscillation around the sphere for six types of deformation: spheroidal shapes and Legendre polynomial ripples P₂, P₃, P₄, P₅, P₆, with relative rms amplitudes of 0.2. Ten different speeds of deformation and eleven different values of the diffuseness of the potential well were studied, making altogether 660 quantal and 660 classical time-dependent calculations. In the upper range of deformation speeds the quantal results for the non-integrable shapes P₃- P₆ agree approximately with the wall formula for dissipation, the deviations being largely accounted for by the wave-mechanical suppression factor of Koonin et al. For low deformation speeds the dissipation becomes dominated by one or two avoided level crossings.