The Coupled-Trajectory Mixed Quantum-Classical Algorithm: A\n Deconstruction

Abstract

We analyze a mixed quantum-classical algorithm recently derived from the\nexact factorization equations [Min, Agostini, Gross, PRL {\\bf 115}, 073001\n(2015)] to show the role of the different terms in the algorithm in bringing\nabout decoherence and wavepacket branching. The algorithm has the structure of\nEhrenfest equations plus a "coupled-trajectory" term for both the electronic\nand nuclear equations, and we analyze the relative roles played by the\ndifferent non-adiabatic terms in these equations, including how they are\ncomputed in practise. In particular, we show that while the coupled-trajectory\nterm in the electronic equation is essential in yielding accurate dynamics,\nthat in the nuclear equation has a much smaller effect. A decoherence time is\nextracted from the electronic equations and compared with that of augmented\nfewest-switches surface-hopping. We revisit a series of non-adiabatic Tully\nmodel systems to illustrate our analysis.\n