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Beyond the Lindblad master equation: Heat, work, and energy currents in boundary-driven spin chains
Luís H Reis1, Saulo H S Silva1, Emmanuel Pereira1
1Departamento de Física-Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, CP 702, 30.161-970 Belo Horizonte MG, Brazil.
Physical Review. E
|July 22, 2020
Summary
Investigating quantum spin systems reveals that heat and work currents can vary while maintaining a constant energy current. Analyzing these boundary-driven systems requires methods beyond the standard Lindblad master equation.
Area of Science:
- Quantum Thermodynamics
- Condensed Matter Physics
- Statistical Mechanics
Background:
- Boundary-driven quantum spin systems are crucial for understanding energy transport in nanoscale devices.
- Accurate characterization of energy, heat, and work currents is essential for quantum thermodynamics.
- The Lindblad master equation is a common tool, but its limitations in complex systems are increasingly recognized.
Purpose of the Study:
- To accurately investigate energy, heat, and work currents in boundary-driven quantum spin systems.
- To explore the relationship between different current components and the total energy current.
- To determine the applicability of the Lindblad master equation for analyzing these currents.
Main Methods:
- Derivation of current expressions and the Lindblad master equation using a repeated interaction scheme.
- Analytical computation of steady-state distributions for small quantum systems.
- Detailed analysis of asymmetrical XXZ and quantum Ising models.
Main Results:
- Identified cases in the XXZ model where varying heat and work currents yield the same energy current.
- Demonstrated a quantum Ising model scenario with zero net energy current but non-vanishing heat and work currents.
- Showcased discrepancies between currents obtained via repeated interaction and those from the Lindblad master equation.
Conclusions:
- The study highlights the necessity of advanced methods beyond the Lindblad master equation for a complete understanding of heat in quantum spin systems.
- Different combinations of heat and work currents can lead to identical energy currents, emphasizing the complexity of energy flow.
- The findings underscore the importance of the chosen theoretical framework in characterizing thermodynamic quantities in quantum systems.
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