Analytical derivation of equilibrium state for open quantum system

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Condensed matter physics

Background:

• Calculating equilibrium states of open quantum systems is computationally intensive due to the large number of bath degrees of freedom.
• Existing methods often struggle with accuracy for complex system-bath interactions.

Purpose of the Study:

• To develop an analytical expression for the reduced density operator of an open quantum system at high temperatures.
• To provide a more tractable method for determining equilibrium states in open quantum systems.

Main Methods:

• Derivation of an analytical expression for the reduced density operator using an effective Hamiltonian.
• Comparison of theoretical predictions with numerically exact results for validation.
• Analysis of the temperature dependence of effective coupling strengths.

Main Results:

• An accurate analytical expression for the reduced density operator is presented for high-temperature, slow-bath regimes.
• The equilibrium state was found to be independent of the spectral density's shape under slow bath conditions.
• Effective coupling strength exhibits exponential dependence on the reorganization energy to temperature ratio.

Conclusions:

• The developed theory offers an accurate and efficient method for calculating equilibrium states in specific open quantum system regimes.
• The findings highlight the crucial role of effective coupling and its temperature dependence in determining system equilibrium.
• This work simplifies the understanding of quantum system dynamics by reducing reliance on complex numerical simulations.