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Fokker-Planck quantum master equation for mixed quantum-semiclassical dynamics.
Jin-Jin Ding1, Yao Wang2, Hou-Dao Zhang2
1School of Chemistry and Chemical Engineering, Nantong University, Nantong, Jiangsu 226019, China.
The Journal of Chemical Physics
|January 16, 2017
Summary
A new Fokker-Planck quantum master equation enhances mixed quantum-classical theory. This improved approach offers broader accuracy for quantum Brownian oscillators, matching the original computational cost.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- The Caldeira-Leggett quantum master equation is foundational for mixed quantum-classical theory but has limited applicability.
- Bridging quantum and classical descriptions in open quantum systems remains a significant challenge.
Purpose of the Study:
- To develop an advanced quantum master equation based on the Fokker-Planck formalism.
- To extend the applicability and accuracy of mixed quantum-classical theories for quantum Brownian oscillators.
Main Methods:
- Formulating a Fokker-Planck quantum master equation incorporating a generic bi-exponential correlation function for environment interactions.
- Developing analytical and numerical parametrization schemes for the bi-exponential environment bath correlation functions.
- Comparing the new theory's predictions against exact dynamics for model systems.
Main Results:
- The proposed Fokker-Planck quantum master equation introduces caustic terms that effectively couple quantum systems to semiclassical environments.
- Various parametrization schemes for the environment bath correlation functions were successfully proposed and analyzed.
- The new theory demonstrates a significantly broadened range of validity and accuracy compared to the original Caldeira-Leggett approach.
Conclusions:
- The Fokker-Planck quantum master equation provides a more versatile and accurate framework for studying quantum Brownian motion in mixed quantum-classical regimes.
- The theory maintains comparable numerical efficiency to existing methods while offering superior performance, particularly at moderately low temperatures.
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