Non-adiabatic Matsubara dynamics and non-adiabatic ring-polymer molecular dynamics.

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Physics

Background:

• Calculating time-correlation functions (TCF) for electronically non-adiabatic systems is computationally challenging.
• Existing methods often struggle with the complex interplay between electronic and nuclear dynamics.

Purpose of the Study:

• To develop a general and rigorous theoretical framework for non-adiabatic quantum dynamics.
• To provide a foundation for improved simulation methods like non-adiabatic ring-polymer molecular dynamics (NRPMD).

Main Methods:

• Derivation of the non-adiabatic Matsubara dynamics formalism from generalized Kubo-transformed TCF.
• Utilizing Wigner representation for nuclear and electronic variables.
• Integration of non-Matsubara nuclear modes and approximations leading to NRPMD.

Main Results:

• The proposed framework rigorously establishes the non-adiabatic Matsubara dynamics approach.
• The non-adiabatic ring-polymer molecular dynamics (NRPMD) method is derived and justified for non-equilibrium TCF simulations.
• Theoretical foundation is laid for recent state-dependent RPMD methods.

Conclusions:

• Non-adiabatic Matsubara dynamics offers a versatile framework for quantum dynamics.
• NRPMD is a validated method for simulating non-adiabatic processes.
• This work advances the development of future non-adiabatic quantum dynamics methods.