Solution to the plateau problem in the Green-Kubo formula

Area of Science:

• Statistical Mechanics
• Computational Physics
• Chemical Physics

Background:

• Transport coefficients in Markovian dynamic equations are typically derived using Green-Kubo formulas.
• These formulas often encounter the 'plateau problem,' where running integrals decay due to variable correlations.
• Existing solutions necessitate extreme timescale separation, limiting applicability.

Purpose of the Study:

• To develop an alternative expression for transport coefficients that circumvents the plateau problem.
• To provide a method for calculating transport coefficients that does not rely on extreme timescale separation.
• To extend the applicability of Green-Kubo-like formulas within the Mori projection operator framework.

Main Methods:

• Utilizing the Mori projection operator formulation.
• Deriving a corrected Green-Kubo expression for transport coefficients.
• Analyzing the behavior of running integrals without assuming extreme timescale separation.

Main Results:

• A novel, corrected Green-Kubo expression for transport coefficients is derived.
• The proposed expression inherently resolves the plateau problem.
• The method is valid even when timescale separation is not extreme, provided the Markovian approximation holds.

Conclusions:

• The corrected Green-Kubo expression offers a robust alternative for calculating transport coefficients.
• This approach expands the utility of Green-Kubo formulas in systems with less pronounced timescale separation.
• The Mori projection operator formulation provides a powerful framework for addressing limitations in statistical mechanics.