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Matsubara dynamics approximation for generalized multi-time correlation functions.

Pablo E Videla¹, Victor S Batista¹

¹Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520-8107, USA.

The Journal of Chemical Physics

|May 8, 2023

Summary

This summary is machine-generated.

We present a semi-classical approximation using Matsubara dynamics to calculate multi-time correlation functions. This method bridges quantum and classical descriptions, showing improved accuracy over classical dynamics for chemical dynamics.

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Area of Science:

Quantum dynamics
Chemical physics
Computational chemistry

Background:

Calculating multi-time correlation functions is crucial for understanding chemical dynamics.
Existing methods face challenges in accurately describing quantum effects in condensed phase systems.
Matsubara dynamics offers a classical approach to conserve quantum Boltzmann distributions.

Purpose of the Study:

To introduce a novel semi-classical approximation for generalized multi-time correlation functions.
To leverage Matsubara dynamics for improved accuracy in quantum dynamics calculations.
To provide a theoretical bridge between quantum and classical descriptions.

Main Methods:

Developed a semi-classical approximation based on Matsubara dynamics.
Expressed generalized multi-time correlation functions as phase-space integrals.
Incorporated classically evolved observables coupled via Poisson brackets in Matsubara space.

Main Results:

The Matsubara approximation shows exactness in zero-time and harmonic limits.
It reduces to classical dynamics with a single Matsubara mode (centroid).
Numerical tests demonstrate superior agreement with exact results compared to classical dynamics.

Conclusions:

The developed method offers a promising semi-classical approach for chemical dynamics.
It serves as a benchmark for future quantum-Boltzmann-preserving approximations.
Addressing the phase problem in Matsubara dynamics is key for practical applications.