Adiabatic Product Expansion

The time-evolution operator for an explicitly time-dependent Hamiltonian is expressed as the product of a sequence of unitary operators. These are obtained by successive time-dependent unitary transformations of the Hilbert space followed by the adiabatic approximation at each step. The resulting adiabatic product expansion yields a generalization of the quantum adiabatic approximation. Furthermore, it leads to an infinite class of exactly solvable models.