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Generalized Gibbs state with modified Redfield solution: exact agreement up to second order
Juzar Thingna1, Jian-Sheng Wang, Peter Hänggi
1Department of Physics and Center for Computational Science and Engineering, National University of Singapore, Singapore 117542, Republic of Singapore. juzar@nus.edu.sg
The Journal of Chemical Physics
|May 23, 2012
Summary
A new method provides accurate steady-state solutions for quantum master equations, matching exact results and simplifying complex quantum system analysis. This approach enhances understanding of quantum dynamics and system-bath interactions.
Area of Science:
- Quantum Mechanics
- Quantum Information Theory
- Statistical Mechanics
Background:
- The Redfield quantum master equation is a standard tool for describing the dynamics of open quantum systems.
- Obtaining accurate steady-state solutions for these equations can be computationally challenging, especially for complex systems.
- Existing methods often require higher-order approximations or approximations that limit their applicability.
Purpose of the Study:
- To develop a novel, computationally efficient scheme for the steady-state solution of the Redfield quantum master equation.
- To achieve agreement with exact results for the reduced density matrix up to second order in system-bath coupling.
- To reduce the numerical complexity of studying large quantum systems.
Main Methods:
- Developed a novel scheme based on analytic continuation of off-diagonal matrix elements of the Redfield solution.
- Applied the method to a heat bath of harmonic oscillators.
- Numerically compared the formulation with the nonequilibrium Green's function formalism for a damped quantum harmonic system.
Main Results:
- The novel scheme yields results in agreement with the exact solution up to second order in system-bath coupling.
- The system correctly relaxes to its coupling-dependent, generalized quantum Gibbs state.
- Good agreement was found with the nonequilibrium Green's function formalism, even for coupling strengths beyond the expected validity of the second-order Redfield equation, particularly at low temperatures.
- The method significantly reduces numerical complexity, enabling efficient study of large system Hilbert spaces.
Conclusions:
- The developed scheme offers an accurate and efficient approach to obtain steady-state solutions for the Redfield quantum master equation.
- This method extends the applicability of Redfield theory to larger coupling strengths and system sizes.
- The findings facilitate the study of quantum dynamics and thermalization in complex quantum systems.
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