Making non-Markovian master equations accessible with approximate environments

Area of Science:

• Quantum Physics
• Computational Chemistry
• Thermodynamics

Background:

• Simulating open quantum systems, especially with non-Markovian dynamics, presents significant computational challenges.
• Existing methods like the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation exhibit inaccuracies at early times and struggle with non-Markovian effects.

Purpose of the Study:

• To develop an accurate and efficient method for simulating non-Markovian dynamics in open quantum systems.
• To demonstrate the utility of expressing environmental correlation functions as sums of damped sinusoidals within master equations.
• To enable straightforward calculation of Lamb-shift corrections, essential for accurate thermodynamic descriptions.

Main Methods:

• Decomposition of the environmental correlation function into a sum of damped sinusoidals.
• Application of this decomposition within master equation formulations.
• Calculation of Lamb-shift corrections without complex principal value integration.

Main Results:

• The proposed method significantly reduces the computational cost of Lamb-shift and decay-rate calculations without sacrificing accuracy.
• Lamb-shift effects were shown to be non-negligible and essential for accurate descriptions in heat transport scenarios.
• The master equation formulations achieved accuracy comparable to numerically exact methods in the weak-coupling regime.

Conclusions:

• The methodology offers a computationally tractable and reliable alternative for simulating non-Markovian dynamics in open quantum systems.
• This approach simplifies the calculation of Lamb-shift corrections, crucial for understanding finite-time thermodynamics.
• The findings pave the way for more efficient and accurate simulations of complex quantum phenomena.