Equivalent Resistance from the Quantum to the Classical Transport Limit

Area of Science:

• Condensed Matter Physics
• Quantum Transport

Background:

• Understanding transport properties in quantum systems is crucial for developing new electronic devices.
• Existing models often struggle to capture the full range of transport phenomena from quantum to classical regimes.
• Electron-phonon and electron-electron interactions significantly complicate the analysis of quantum networks.

Purpose of the Study:

• To generalize the concept of equivalent resistance to encompass both quantum and classical transport regimes.
• To introduce a novel framework, transport equivalent networks, for simplifying complex quantum network structures.
• To demonstrate how this framework preserves essential global and local transport properties under various interaction strengths.

Main Methods:

• Generalization of equivalent resistance to define transport equivalent networks.
• Analysis of quantum network structures and their transport properties.
• Inclusion of electron-phonon and electron-electron interactions within the framework.

Main Results:

• The proposed transport equivalent networks simplify quantum network structures effectively.
• Global and local transport properties are preserved even with significant interaction effects.
• A clear evolutionary path from equivalent quantum networks to classical resistor networks is established with increasing interaction strength.

Conclusions:

• Transport equivalent networks offer a powerful platform for analyzing and simplifying quantum transport phenomena.
• This approach provides a unified view of transport across quantum and classical regimes.
• The framework facilitates the understanding of how interactions modify transport behavior in condensed matter systems.