Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness...

Area of Science:

• Quantum dynamics
• Theoretical physics
• Chemical physics

Background:

• The Caldeira-Leggett approach is a foundational method for quantum dissipation.
• Previous models often simplified bath interactions, neglecting crucial nonequilibrium and non-Markovian effects.

Purpose of the Study:

• To derive a generalized quantum Fokker-Planck equation (GQFPE) for photo-induced quantum dynamical processes.
• To consistently incorporate nonequilibrium and non-Markovian effects using an extended path integral method.
• To analyze the properties and limits of the derived GQFPE.

Main Methods:

• Extension of the Caldeira-Leggett path integral method.
• Utilization of a nonequilibrium influence functional for different electronic states.
• Second-order expansion of paths in the influence functional exponents.
• Short-time expansion of effective action and Gaussian integration.

Main Results:

• A novel GQFPE is derived, incorporating time-dependent kernels and boundary terms.
• The derived equation is shown to be in the Dekker form.
• Analysis for an Ohmic spectral density with Drude cutoff confirms positive definiteness in relevant temperature regimes.
• The steady-state limit approaches the Caldeira-Leggett expression with added quantum and non-Markovian corrections.

Conclusions:

• The developed GQFPE provides a more comprehensive framework for studying photo-induced quantum dynamics.
• The inclusion of boundary terms, though complicating derivation, is essential for accurate dynamics.
• The GQFPE offers improved accuracy over previous models, especially under non-Markovian and nonequilibrium conditions.