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

Abstract

We perform quantum trajectory simulations of the decay dynamics of initially localized 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 (ITR), set at infinity, is found to have a moderate influence on the accuracy of the ITR 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.