Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

Understand

We solve the non-stationary Schrodinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models.

• The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models.
• We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field.
• Moreover, we demonstrate that the time-dependent Schrodinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnikov-Zamolodchikov equations.