Dissipation in small systems: Landau-Zener approach

Area of Science:

• Quantum thermodynamics
• Statistical mechanics
• Condensed matter physics

Background:

• Stochastic thermodynamics provides a framework for understanding energy, work, and heat in small systems.
• Fermionic systems and their interactions with reservoirs are crucial in quantum computing and materials science.
• Landau-Zener theory describes transitions between quantum states during avoided crossings.

Purpose of the Study:

• To establish a stochastic thermodynamic framework for a driven Fermionic level.
• To analyze the system dynamics and thermodynamics under time-dependent driving.
• To identify and quantify energy, work, heat, entropy, and dissipation in the system.

Main Methods:

• Developing a stochastic thermodynamics for a driven Fermionic level.
• Utilizing Landau-Zener theory to describe avoided crossings between system and reservoir levels.
• Employing a two-point measurement approach to obtain numerically exact quantum work statistics.

Main Results:

• Derived system dynamics and thermodynamic quantities (energy, work, heat, entropy, dissipation).
• Achieved perfect agreement between theoretical predictions and numerically exact quantum work statistics.
• Provided an explicit expression for dissipation in terms of diabatic transitions.

Conclusions:

• The developed stochastic thermodynamics accurately describes driven Fermionic systems.
• The theory successfully links dissipation to diabatic transitions in the system-reservoir interaction.
• This work offers a robust theoretical tool for analyzing quantum thermodynamics in driven systems.