New phase space formulations and quantum dynamics approaches

Abstract

We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discretevariable quantum systems. This leads to a general coordinate-momentum phase space formulation of composite quantum systems, where conventional representations on infinite phase space are employed for continuous variables. It is convenient to utilize (weighted) constraint coordinate-momentum phase space for representing the quantum state and describing nonclassical features. Various numerical tests demonstrate that new trajectorybased quantum dynamics approaches derived from the (weighted) constraint phase space representation are useful and practical for describing dynamical processes of composite quantum systems in gas phase as well as in condensed phase.

Transition Path Flight Times and Nonadiabatic Electronic Transitions

“…The resonance effects and other time-domain phenomena presented show FSSH results will match fully quantum ones more closely if one broadens the incident wavepacket considerably such that quantum coherence effects are diminished. We expect that a similar conclusion applies to other trajectory-based approximate methods. − ,− ,, It will be interesting to see whether it is possible to further improve upon surface hopping, − ,, phase space mapping dynamics approaches, − ,− and other trajectory-based nonadiabatic methods so that they can capture the type of resonance effects described in this Letter.…”

“…We expect that a similar conclusion applies to other trajectory-based approximate methods. [31][32][33][56][57][58][59][60][61][62]65,66 It will be interesting to see whether it is possible to further improve upon surface hopping, [37][38][39][40][41][42]65,66 phase space mapping dynamics approaches, 31−33,59−62 and other trajectory-based nonadiabatic methods so that they can capture the type of resonance effects described in this Letter.…”

“…In this context, we have shown previously that a weak-value-based mean time, , called the transition path flight time, is a useful way to probe the time domain in the study of quantum transitions, notably in measuring transition times and demonstrating their connection to phase times in the context of tunneling. ,, Here, we perform similar analysis to calculate the flight times associated with highly nonadiabatic transitions in a one-dimensional, two-level model system. Quantum effects such as tunneling, resonance and classically forbidden transitions are expected to play significant roles in determining these times in such systems. − In particular, we calculate mean times and accompanying time distributions associated with the transmission and reflection subensembles on both of the two surfaces, alongside the associated transmission and reflection probabilitiesstudying these time-domain quantities reveals new physical insights that the probabilities alone fail to divulge.…”

“…The comparison between the QM and FSSH results is useful in elucidating where and how quantum effects are important in determining the mean times and the flight time distributions. We suspect that comparison with other quasi-classical approximate methods − ,− would reveal similar differences, as all such approximations do not include phases and quantum superposition. Although the present study was limited to what is arguably the simplest possible model, we expect that the effects considered here can sometimes become important when considering scattering with multiple surfaces or crossings, or in multidimensional systems where interferences cannot be ignored in the electronic transmission process.…”

Nonadiabatic Couplings Can Speed Up Quantum Tunneling Transition Path Times

“…Nonadiabatic effects play important roles in many chemical reactions, and the dynamics of these systems has been studied extensively both quantum mechanically and otherwise. − However, the time-domain properties of systems such as avoided crossings have received comparatively little attention.…”