Quantum tunneling dynamics in multidimensional systems: a matching-pursuit description.

Rigorous simulations of quantum tunneling dynamics in model systems with up to 20 coupled degrees of freedom are reported. The simulations implement an extension of the recently developed matching-pursuit/split-operator Fourier-transform method to complex-valued coherent-state representations. The resulting method recursively applies the time-evolution operator, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state representations generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method.