On Exact Solutions of Novel Multistate Landau-Zener Problems.

A multistate Landau-Zener (MLZ) Hamiltonian is used to model numerous non-equilibrium experiments involving cold atoms, quantum dots and quantum dot molecules. We recently showed that all the known MLZ problems either reduce to the $2 \times 2$ Landau Zener problem or belong to a family of mutually commuting Hamiltonians (that are polynomial in time).\footnote{A. Patra and E. A. Yuzbashyan, J. Phys. A: Math. Theor. {\bf 48}, 245303 (2015).} Based on this classification we identify previously unknown MLZ problems, explicitly obtain their solutions and discuss relevant experimental scenarios.