Path integral based calculations of symmetrized time correlation functions. I.

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Computational chemistry

Background:

• Calculating correlation functions is crucial in many areas of physics and chemistry.
• Approximating quantum evolution with classical dynamics offers computational advantages.
• Schofield's symmetrized time correlation function is a key quantity for such studies.

Purpose of the Study:

• To investigate the conditions and methods for approximating quantum evolution using classical dynamics.
• To analyze the role of quantum delocalization in the accuracy of these approximations.
• To provide a path integral-based derivation of Schofield's quantum correction factor.

Main Methods:

• Expressing Schofield's correlation function as a path integral in complex time.
• Utilizing sum and difference path variables.
• Performing Taylor series expansion of the path integral exponent to first and second order.

Main Results:

• A novel, path integral-based derivation of Schofield's quantum correction factor was achieved via first-order expansion.
• Second-order expansion revealed how quantum mechanical delocalization impacts correlation function approximations.
• The study demonstrates limitations in interpreting propagators as classical trajectories due to quantum effects.

Conclusions:

• Classical dynamics approximations for quantum evolution in correlation functions are feasible but have limitations.
• Quantum delocalization inherently complicates the semiclassical interpretation of propagators.
• Further theoretical development is needed to fully reconcile quantum and classical descriptions in these calculations.