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A new method improves Hierarchical Equations of Motion (HEOM) calculations for open quantum dynamics by accurately treating bath mode delocalization. This enhances efficiency, especially for fast baths and at low temperatures.

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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.