Exploiting the path-integral radius of gyration in open quantum dynamics

Area of Science:

• Quantum Dynamics
• Computational Physics
• Theoretical Chemistry

Background:

• Open quantum dynamics calculations face challenges including Matsubara-decay terms.
• These terms arise from bath mode delocalization, quantified by the radius of gyration squared R2(ω).
• In Hierarchical Equations of Motion (HEOM), R2(ω) is often approximated.

Purpose of the Study:

• To investigate the role of R2(ω) in HEOM calculations.
• To develop more efficient HEOM methods for open quantum systems.
• To improve the treatment of bath dynamics in quantum simulations.

Main Methods:

• Analysis of the Ishizaki-Tanimura correction in relation to R2(ω) contributions.
• Modification of the correction for improved efficiency with fast baths.
• Development of an "A4" algorithm, an adaptation of the adaptive Antoulas-Anderson (AAA) algorithm, for fitting R2(ω).

Main Results:

• The Ishizaki-Tanimura correction separates smooth and "Brownian" parts of R2(ω).
• Modifying this correction enhances HEOM efficiency for fast baths.
• The "A4" algorithm enables efficient fitting of R2(ω) to a sum over poles.
• This leads to highly efficient standard HEOM implementation at low temperatures.

Conclusions:

• Accurate treatment of bath mode delocalization is crucial for HEOM.
• The proposed modifications and "A4" algorithm offer significant efficiency gains.
• This work provides a more robust and efficient approach to simulating open quantum dynamics, particularly at low temperatures.