Quantum dynamics for weakly anharmonic systems from genuinely classical trajectories

Abstract

We present a new approach to the treatment of the dispersion of a quantum wave packet in a weakly anharmonic multidimensional potential. It assumes mapping of the quantum problem on its classical counterpart, the latter being solvable, by assumption, in the action-angle variables. The semiclassical quantization of the action variables allows us to construct a special class of quantum states that we dub scrambled coherent states. These states provide the possibility to compute the observables and their correlations with a fair accuracy, also at times when the dispersion of a wave packet due to the anharmonicity of the potential becomes dominant. The numerical estimation of the coefficients determining the scrambled coherent dynamics is of polynomial complexity and thus opens the way to avoid the ‘curse of dimensionality’.