Many-body dynamics with time-dependent interaction

Recent advances in optical Feshbach resonance technique have enabled the experimental investigation of atomic gases with time-dependent interaction. In this work, we study many-body dynamics weakly interacting bosons subject an arbitrary time varying scattering length. By employing a variational ansatz, derive effective Hamiltonian that governs thermal particles. Crucially, show there exists hidden symmetry can map to precession SU(1,1) "spin". As demonstration, calculate situation where length is sinusoidally modulated. We non-compactness group naturally leads solutions exponentially growth Bogoliubov modes and causes instabilities.