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Stochastic equation of motion approach to fermionic dissipative dynamics. I. Formalism
Lu Han1, Arif Ullah1, Yun-An Yan2
1Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
The Journal of Chemical Physics
|June 4, 2020
Summary
We developed a new method, Minimal Auxiliary Space-Stochastic Equation of Motion (MAS-SEOM), for simulating fermionic open systems. This approach accurately models complex environmental interactions at ultra-low temperatures.
Area of Science:
- Quantum Mechanics
- Condensed Matter Physics
- Computational Chemistry
Background:
- Accurate simulation of fermionic open systems is crucial for understanding quantum phenomena.
- Dissipative dynamics in these systems are challenging due to environmental interactions.
- Stochastic Equation of Motion (SEOM) theory offers a framework but faces numerical challenges.
Purpose of the Study:
- To develop a numerically feasible method for simulating fermionic open systems.
- To address the challenge of realizing time-dependent Grassmann fields in SEOM theory.
- To provide an accurate and efficient approach for studying systems at ultra-low temperatures.
Main Methods:
- Established formally exact Stochastic Equation of Motion (SEOM) theory.
- Introduced a Minimal Auxiliary Space (MAS) mapping scheme to represent stochastic Grassmann fields.
- Developed the numerically feasible MAS-SEOM method by mapping Grassmann fields to c-number fields and pseudo-levels.
Main Results:
- The MAS-SEOM method enables numerical realization of stochastic Grassmann fields.
- Analysis connects MAS-SEOM properties to established time-dependent perturbation theory and hierarchical equations of motion.
- The method is shown to be accurate and efficient for simulating fermionic open systems.
Conclusions:
- The MAS-SEOM method provides a significant advancement in simulating fermionic open systems.
- This approach is particularly promising for studies at ultra-low temperatures.
- It offers a computationally tractable pathway for exploring complex quantum dynamics.
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