Real-time dynamics with bead-Fourier path integrals. I. Bead-Fourier CMD

Area of Science:

• Condensed Matter Theory
• Computational Quantum Chemistry
• Materials Science

Background:

• Calculating real-time quantum correlation functions is a major challenge in condensed matter physics.
• Centroid Molecular Dynamics (CMD) uses Feynman Path Integrals (PIs) to incorporate nuclear quantum effects into classical simulations.
• Conventional CMD employs discretized PIs, representing quantum particles as 'beads' in a ring polymer.

Purpose of the Study:

• To develop a more efficient method for calculating quantum correlation functions.
• To improve the accuracy and reduce the computational cost of molecular dynamics simulations involving quantum effects.
• To introduce a novel CMD approach utilizing Bead-Fourier PIs (BF-PIs).

Main Methods:

• The study presents a new CMD method employing the Bead-Fourier Path Integral (BF-PI) formalism.
• BF-PIs represent imaginary time paths using a Fourier sine series, acting as an intermediate between discretized PIs and pure Fourier methods.
• The effective potential is calculated using BF-PIs instead of traditional bead PIs.

Main Results:

• The new BF-CMD method demonstrates accuracy and efficiency for 1D model systems.
• At low temperatures, BF-CMD achieved a fourfold to eightfold reduction in the number of beads required for convergence.
• This efficiency gain was realized with the addition of just a single Fourier component.

Conclusions:

• The developed BF-CMD methodology offers a significant computational advantage for simulating quantum dynamics.
• The approach effectively reduces the number of beads needed, particularly at low temperatures.
• This general method can be extended to other path integral methods like Ring Polymer Molecular Dynamics and non-adiabatic PI methods.