Exact open quantum system dynamics: Optimal frequency vs time representation of bath correlations

Area of Science:

• Quantum Mechanics
• Computational Physics

Background:

• Accurate simulation of open quantum systems is crucial for understanding complex phenomena.
• Existing numerical methods face challenges in representing bath correlations effectively.

Purpose of the Study:

• To evaluate the suitability of different bath correlation representations for numerically exact open quantum system dynamics.
• To compare the Hierarchy of Pure States (HOPS) and multi-Davydov-Ansatz methods.
• To identify optimal discretization strategies for spectral densities.

Main Methods:

• Discussed two numerically exact methods: Hierarchy of Pure States (HOPS) and multi-Davydov-Ansatz.
• Focused on the representation of bath correlation functions (BCF).
• Analyzed the spin-boson model with a sub-Ohmic spectral density.

Main Results:

• The quality of BCF description in the time domain is critical for HOPS.
• A windowed Fourier transform of the BCF indicates discretization quality for multi-Davydov-Ansatz.
• An exponential distribution-based discretization of the spectral density proved most favorable.

Conclusions:

• The choice of BCF representation significantly impacts the accuracy of open quantum system simulations.
• The multi-Davydov-Ansatz benefits from spectral density discretization informed by Fourier analysis.
• Exponential discretization offers a favorable approach for the studied spin-boson model.