Transition Path Flight Times and Nonadiabatic Electronic Transitions

Abstract

Transition path flight times are studied for scattering on two electronic surfaces with a single crossing. These flight times reveal nontrivial quantum effects such as resonance lifetimes and nonclassical passage times and reveal that nonadiabatic effects often increase flight times. The flight times are computed using numerically exact time propagation and compared with results obtained from the Fewest Switches Surface Hopping (FSSH) method. Comparison of the two methods shows that the FSSH method is reliable for transition path times only when the scattering is classically allowed on the relevant adiabatic surfaces. However, where quantum effects such as tunneling and resonances dominate, the FSSH method is not adequate to accurately predict the correct times and transition probabilities. These results highlight limitations in methods which do not account for quantum interference effects, and suggest that measuring flight times is important for obtaining insights from the time-domain into quantum effects in nonadiabatic scattering.

Nonadiabatic Couplings Can Speed Up Quantum Tunneling Transition Path Times

“…It is interesting to note that in the resonance region, there appears to be a hint of a fifth resonance right below the opening of the upper threshold at 0.02 atomic units of energy, something which is not seen in the transmission probability. This could be due to a fifth, rather shallow bound state in the upper potential well (this possibility was not ruled out in our previous work). There is though the possibility that it is a numerical artifact of the methods usedthe asymptotic region may not have been placed far enough out to treat the channel as properly closed just below the threshold, leading to a “tunneling-like” effect where there is none physically.…”

“…The relative error between the two calculation methods never differs by more than 4 × 10 −5 . The resonance positions match those in our previous work; 48 however, the resonance widths are much smaller due to the lack of energy averaging of an initial wave packet. sufficiently small and the x-range sufficiently large to account for this (likewise, the time steps were sufficiently small and the initial position sufficiently far from the interaction region).…”

“…The relative error between the two calculation methods never differs by more than 4 × 10 –5 . The resonance positions match those in our previous work; however, the resonance widths are much smaller due to the lack of energy averaging of an initial wave packet.…”

“…Previously, we have analyzed tunneling times for one-dimensional, one-state systems, − defining a metric called the tunneling flight time. This measure considers the time it takes particles characterized by incident Gaussian wavepackets to traverse a barrier and hit a screen.…”

“…Recently, we started exploring temporal properties of quantum transitions in nonadiabatic systems. We focused on a comparison between the numerically exact quantum determination of flight times and the results obtained with approximate quasi-classical methods such as surface hopping. − These methods have a history of being applied to nonadiabatic systems , as well as systems with non-Born–Oppenheimer corrections , and tunneling .…”