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Mean field dynamics of some open quantum systems
Marco Merkli1, Alireza Rafiyi1
1Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland and Labrador, Canada A1C 5S7.
Proceedings. Mathematical, Physical, and Engineering Sciences
|May 10, 2018
Summary
This study develops a new expansion for quantum system averages, analyzing observable dynamics for large particle numbers. The findings are applicable to quantum optics and energy-conserving models.
Area of Science:
- Quantum mechanics
- Statistical physics
Background:
- Understanding the behavior of large quantum systems interacting with a reservoir is crucial.
- Mean-field interactions simplify complex many-body quantum dynamics.
Purpose of the Study:
- To derive an expansion for averages of observables in quantum systems with mean-field interactions.
- To analyze the dynamics of these observables in the limit of large particle numbers.
Main Methods:
- Utilizing the Dyson series expansion of the propagator.
- Analyzing the system in the limit of large N (number of particles).
Main Results:
- An expansion for averages of observables (both particles and reservoir) in inverse powers of N.
- Detailed analysis of the dynamics of n-particle observables, extensive observables, fluctuations, and reservoir observables.
Conclusions:
- The derived expansion provides a powerful tool for studying large quantum systems.
- The results are illustrated using the infinite mode Dicke model and energy-conserving models.
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