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Large deviations and fluctuation theorem for the quantum heat current in the spin-boson model
Erik Aurell1, Brecht Donvil2, Kirone Mallick3
1KTH Royal Institute of Technology, AlbaNova University Center, SE-106 91 Stockholm, Sweden and Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland.
Physical Review. E
|June 25, 2020
Summary
This study derives a heat current generating function for a qubit coupled to harmonic oscillator baths. The function satisfies fluctuation theorems and confirms the fluctuation-dissipation relation, providing numerical heat current results.
Area of Science:
- Quantum thermodynamics
- Open quantum systems
- Spin-boson interactions
Background:
- Understanding heat transport in quantum systems is crucial for quantum technologies.
- The spin-boson model describes a fundamental interaction between a quantum system and its environment.
- Path integral methods are powerful tools for analyzing quantum dynamics.
Purpose of the Study:
- To derive an explicit expression for the heat current generating function in a qubit-environment system.
- To verify the validity of the Gallavotti-Cohen fluctuation theorem for this system.
- To investigate the relationship between heat conductance and current fluctuations.
Main Methods:
- Feynman-Vernon path integral evaluation
- Noninteracting blip approximation (NIBA)
- Polaron transform comparison
- Numerical analysis of heat current
Main Results:
- An explicit expression for the heat current generating function was derived using NIBA.
- The derived function satisfies the Gallavotti-Cohen fluctuation theorem.
- Heat conductance was found to be proportional to the variance of the heat current, confirming the fluctuation-dissipation relation.
Conclusions:
- The study successfully derived and verified key theoretical results for quantum heat transport.
- The methods employed provide a robust framework for analyzing similar quantum thermodynamic systems.
- Numerical results offer insights into the behavior of heat current in this specific spin-boson model.
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