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Quantum entanglement and the Born-Markov approximation for an open quantum system.
1Kirensky Institute of Physics, 660036 Krasnoyarsk, Russia and Siberian Federal University, 660041 Krasnoyarsk, Russia.
Physical Review. E
|July 22, 2020
Summary
This study validates the Born-Markov approximation for open quantum systems using a chaotic Bose-Hubbard chain model. Strong bath ergodicity justifies the approximations needed for deriving the Markovian master equation.
Area of Science:
- Quantum mechanics
- Open quantum systems
- Quantum chaos
Background:
- The Born-Markov approximation is crucial for describing open quantum systems.
- Its validity often relies on assumptions about the bath's properties.
- A microscopic understanding of these properties is needed.
Purpose of the Study:
- To rigorously justify the Born-Markov approximation.
- To investigate the role of bath properties in Markovian dynamics.
- To connect quantum chaos in the bath to the validity of the approximation.
Main Methods:
- Utilizing a microscopic model: the Bose-Hubbard chain.
- Analyzing the bath in a quantum chaotic parameter regime.
- Examining the ergodic properties of the bath.
Main Results:
- Demonstrated that strong ergodic properties of the Bose-Hubbard chain bath are key.
- Showed these properties rigorously justify the approximations in the Born-Markov approach.
- Established a first-principles derivation of the Markovian master equation.
Conclusions:
- The quantum chaotic nature of the bath provides a solid foundation for the Born-Markov approximation.
- Ergodicity in the bath is sufficient to derive Markovian master equations.
- This work offers a microscopic justification for a fundamental tool in open quantum system theory.
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