Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating...

Area of Science:

• Physics
• Physical Chemistry
• Statistical Mechanics

Background:

• The generalized Langevin equation (GLE) models particle dynamics interacting with a bath.
• Existing studies on GLE and fluctuation-dissipation theorem (FDT) are limited to time-independent forces or single-particle responses to fields.
• Particle-bath systems are crucial for understanding phenomena from condensed matter to biological processes.

Purpose of the Study:

• To extend the generalized Langevin equation (GLE) and fluctuation-dissipation theorem (FDT) to a more general scenario.
• To investigate systems where both the tagged particle and bath oscillators are subject to an external time-dependent oscillatory field.
• To analyze the behavior of charged or polarizable particles in a similar environment under an AC electric field.

Main Methods:

• Derivation of the generalized Langevin equation (GLE) from a particle-bath Hamiltonian.
• Extension of the fluctuation-dissipation theorem (FDT) to include coupled particle-bath responses to external fields.
• Analysis of the ensemble average of the stochastic force under AC electric fields.

Main Results:

• The ensemble average of the stochastic force is non-zero and proportional to the AC field.
• A modified FDT is derived: 〈F_{P}(t)F_{P}(t^{'})〉=mk_{B}Tν(t-t^{'})+(γe)^{2}E(t)E(t^{'}).
• The derived FDT incorporates the friction memory function and the influence of the external field.

Conclusions:

• The study successfully extends GLE and FDT to coupled particle-bath systems under external oscillatory fields.
• The findings are applicable to systems like charged particles in AC electric fields.
• This work provides a more comprehensive theoretical framework for non-Markovian dynamics in driven systems.