Long-Time-Step Integrators for Almost-Adiabatic Quantum Dynamics

The highly oscillatory solution of a singularly perturbed Schrodinger equation with time-dependent Hamiltonian is computed numerically. The new time-symmetric integrators presented here can be used efficiently with step sizes significantly larger than those required by traditional schemes. This is achieved by a transformation of the problem and an expansion technique for integrals over the oscillating components. The error behavior in the adiabatic case is thoroughly analyzed, and the performance of the methods is illustrated both in an almost-adiabatic setup and in an avoided energy level crossing, where nonadiabatic state transitions occur.

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