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Non-Markovian linear response theory for quantum open systems and its applications
H Z Shen1,2, D X Li1, X X Yi1,2
1Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China.
Physical Review. E
|February 18, 2017
Summary
We derived a new formula for open system linear response applicable to both Markovian and non-Markovian dynamics. This method allows controlling system response, with applications in quantum statistical mechanics and condensed matter physics.
Area of Science:
- Condensed Matter Physics
- Quantum Statistical Mechanics
Background:
- The Kubo formula describes linear response in closed systems.
- Extensions to open systems typically rely on the Markovian approximation.
- Non-Markovian dynamics in open systems remain less explored.
Purpose of the Study:
- Derive a linear response formula for open systems under non-Markovian dynamics.
- Develop a unified framework applicable to both Markovian and non-Markovian regimes.
- Investigate the control of system response through environmental spectral density.
Main Methods:
- Derivation of a general linear response formula for open systems.
- Analysis of system dynamics based on environmental spectral density parameters.
- Application to Hall conductance in a two-band tight-binding model.
Main Results:
- A novel response formula valid for both Markovian and non-Markovian dynamics was derived.
- Hall conductance in a two-band system was calculated, demonstrating environmental influence.
- Modulating the environment's spectral density was shown to transition Hall conductance between Markovian and non-Markovian regimes.
Conclusions:
- The derived formula provides a versatile tool for studying open quantum systems.
- Environmental spectral density can be used to control system response, specifically Hall conductance.
- This work offers potential applications in quantum statistical mechanics and condensed matter physics.
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