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Related Experiment Video

Updated: Jul 15, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit.

Vinod Krishna¹

¹Department of Physics, Yale University, New Haven, Connecticut 06520, USA. vkrishna@hec.utah.edu

The Journal of Chemical Physics

|April 14, 2007

Summary

This study reveals geometric effects on quantum dynamics in Born-Oppenheimer systems. It offers a method to improve mixed quantum-classical approximations using stationary phase approximations.

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Area of Science:

Quantum dynamics
Theoretical chemistry
Chemical physics

Background:

Nonadiabatic couplings significantly influence molecular dynamics.
Accurate modeling of these dynamics is crucial for understanding chemical reactions.
Existing mixed quantum-classical methods often lack rigorous quantum corrections.

Purpose of the Study:

To identify geometric effects on dynamics from nonadiabatic couplings in Born-Oppenheimer systems.
To develop a systematic method for deriving corrections to mixed quantum-classical approaches.
To provide a rigorous quantum mechanical description of nuclear dynamics influenced by electronic nonadiabatic coupling.

Main Methods:

Exact path integral formulation for quantum nonadiabatic dynamics.
Stationary phase approximations to the quantum propagator.
Analysis within the Ehrenfest framework.
Comparison with the fewest switches surface hopping method.

Main Results:

Quantum corrections to mixed quantum-classical methods are derived via stationary phase approximations.
A rigorous description of quantum corrections due to electronic nonadiabatic coupling on nuclear dynamics is obtained.
The fewest switches surface hopping method is identified as a quasiclassical approximation.

Conclusions:

Geometric effects play a key role in nonadiabatic dynamics.
The proposed method offers a systematic way to incorporate quantum corrections into semiclassical simulations.
Semiclassical extensions are suggested for including classically forbidden nonadiabatic transitions.