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Complete positivity and thermal relaxation in quadratic quantum master equations
1Instituto de Física, <a href="https://ror.org/03490as77">Universidade Federal do Rio de Janeiro</a>, Rio de Janeiro, RJ 21941-972, Brazil.
Physical Review. E
|December 18, 2024
Summary
This study develops a systematic method for quantum master equations that ensure complete positivity and trace preservation (CPTP) for thermal relaxation. A CPTP criterion is established for many-body quadratic Hamiltonians, applicable to interacting systems like quantum heat conduction models.
Area of Science:
- Quantum Physics
- Statistical Mechanics
- Quantum Information Theory
Background:
- Quantum master equations describe the dynamics of open quantum systems.
- Ensuring complete positivity and trace preservation (CPTP) is crucial for physical realism.
- Thermal relaxation processes are fundamental in understanding system dynamics.
Purpose of the Study:
- To develop a systematic method for deriving quantum master equations satisfying CPTP requirements.
- To describe thermal relaxation processes within this framework.
- To establish a CPTP criterion for a specific class of quantum master equations.
Main Methods:
- Canonical quantization of generalized Brownian motion.
- Analysis of many-body quadratic Hamiltonians.
- Derivation of a CPTP criterion.
Main Results:
- A systematic method for deriving CPTP quantum master equations is presented.
- The derived dynamics classically describe thermal relaxation.
- A specific CPTP criterion is established for many-body quadratic Hamiltonians.
Conclusions:
- The developed method provides a way to construct physically consistent quantum master equations.
- The established CPTP criterion is applicable to complex models, including those with interactions.
- This work facilitates the study of quantum effects on phenomena like heat conduction.
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