Adiabatic molecular dynamics: Two-body and many-body aspects

We compare various types of adiabatic dynamics that occur during atomic collisions and molecular dynamics. Born-Oppenheimer and non-adiabatic effects in molecular dynamics are contrasted with the time-dependent Landau-Zener transition problem for transitions that occur when a parameter in the Hamiltonian is varied slowly, and these are contrasted with the coherent many-body transitions that occur for a degenerate gas of atoms when an external parameter is tuned slowly near a Feshbach resonance to create loosely bound molecules. Analysis of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms shows that the dependence of the remaining atomic fraction on the sweep rate varies from exponential Landau-Zener behaviour for a single pair of particles to a power-law dependence for large particle number N.