In the emerging field of coherent many-body dynamics, we seek to understand the behavior of an isolated quantum many-body system driven far from equilibrium by changing its Hamiltonian in time. In this talk, I will identify a general class of many-body and matrix Hamiltonians for which this problem is exactly solvable. In particular, I will outline a way to make the parameters (e.g., the interaction strength) of certain quantum integrable models time-dependent without breaking their integrability.

Interesting many-body models that emerge from this approach include a superconductor with the interaction strength inversely proportional to time, a Floquet BCS superconductor, and the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance as well as various models of multi-level Landau-Zener tunneling. I will solve the non-stationary Schrodinger equation exactly for all these models and discuss some interesting physics that emerges at large times.