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Asymptotic large deviations of counting statistics in open quantum systems
1School of Physics, Beihang University, Beijing 100191, China.
Physical Review. E
|January 20, 2024
Summary
We calculated large deviations in quantum systems using a semi-Markov process. Results reveal universal formulas for large deviation rates in open quantum systems at zero and large currents.
Area of Science:
- Quantum optics
- Statistical mechanics
- Quantum information theory
Background:
- Open quantum systems exhibit complex dynamics influenced by their environment.
- Counting statistics are crucial for understanding information flow and correlations in quantum systems.
- Large deviation theory provides a framework to analyze rare events and extreme fluctuations.
Purpose of the Study:
- To calculate large deviations of counting statistics for three distinct open quantum systems.
- To investigate the behavior of large deviation rate functions at zero and large currents.
- To explore the role of non-Hermitian Hamiltonians in quantum statistical properties.
Main Methods:
- Utilizing a semi-Markov process to model the dynamics of open quantum systems.
- Deriving and solving scaled cumulant generating functions for the systems.
- Analyzing the eigenvalues of non-Hermitian Hamiltonians.
Main Results:
- Exact solutions for scaled cumulant generating functions were obtained for two systems (two-level and Λ-configuration three-level).
- Asymptotic large deviations were derived for a V-configuration three-level system, despite the complexity of a sixth-degree polynomial equation.
- Identified that large deviation rate functions at zero current equal twice the largest non-zero real parts of eigenvalues of -iĤ.
- Established a unified formula for these functions at large currents.
Conclusions:
- The semi-Markov process is effective for analyzing large deviations in various open quantum systems.
- The derived formulas offer insights into the statistical properties and fluctuations within these quantum systems.
- Results highlight a universal behavior of large deviation rate functions in open quantum systems under different current conditions.
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