Multi-time formulation of Matsubara dynamics

Area of Science:

• Quantum Dynamics
• Statistical Mechanics
• Computational Physics

Background:

• Matsubara dynamics is a key theory for single-time correlation functions.
• Calculating multitime correlation functions in quantum systems is complex.
• Existing methods often lack generalizability for higher-order functions.

Purpose of the Study:

• To generalize Matsubara dynamics for multitime correlation functions.
• To establish a benchmark theory for Boltzmann-preserving semiclassical approximations.
• To explore the connection between path integral imaginary time-ordering and classical dynamics.

Main Methods:

• Extension of the Matsubara approximation to two-time correlation functions.
• Generalization to multitime fully symmetrized Kubo transformed correlation functions.
• Development of a multitime Matsubara dynamics approximation.

Main Results:

• The Matsubara approximation is applicable to two-time correlation functions.
• A multitime Matsubara dynamics approximation for multitime correlation functions is derived.
• A connection between imaginary time-ordering and classical dynamics is revealed.

Conclusions:

• The generalized multitime Matsubara dynamics provides a benchmark for future semiclassical approximations.
• This formulation highlights the link between quantum path integrals and classical dynamics.
• Further development is needed for practical applications due to a phase-term.