Interacting trajectory representation of quantum dynamics: Influence of boundary conditions on the tunneling decay of resonant states

We perform quantum trajectory simulations of the decay dynamics of initially localised resonant states. Quantum dynamics is represented by a swarm of interacting trajectories which maps the originally quantum problem into the motion of an equivalent (higher-dimensional) classical system. We address two model problems, in which the decay of the initial resonance leads to either spatially confined or asymptotically free wave-packet dynamics, specifically on a double well potential and on a potential plain. The traditional choice of fixed boundary conditions in the interacting trajectory representation, set at infinity, is found to have a moderate influence on the accuracy of the interacting trajectory representation of quantum trajectory dynamics, for the motion on a double well potential, i.e., the results of the trajectory-based scheme are in good correspondence with those obtained via quantum wave-packet propagation up to several fundamental vibrational periods. On the other hand, standard boundary conditions have negligible effect on the interacting trajectory dynamics of a decaying shape resonance, whose predictions reproduce quantum mechanical results at long times.