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Updated: May 18, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Generalized Caroli formula for the transmission coefficient with lead-lead coupling
Huanan Li1, Bijay Kumar Agarwalla, Jian-Sheng Wang
1Department of Physics and Center for Computational Science and Engineering, National University of Singapore, Singapore 117542, Republic of Singapore. g0900726@nus.edu.sg
We developed a new formula for transmission coefficients in lead-junction-lead systems, accounting for lead interactions. This generalized formula simplifies calculations for heat and electrical transport in ballistic systems.
Area of Science:
- Condensed Matter Physics
- Quantum Transport
Background:
- Understanding electron and heat transport in nanoscale systems is crucial.
- Existing models often simplify or neglect interactions between system components.
Purpose of the Study:
- To derive a generalized transmission coefficient formula for lead-junction-lead systems.
- To incorporate interactions between leads into the formula.
- To explore applications in heat and electrical transport.
Main Methods:
- Development of a generalized transmission coefficient formula.
- Mathematical derivation and analysis of the formula's validity.
- Application to ballistic transport systems and interface problems.
Main Results:
- A generalized transmission coefficient formula is presented, accounting for lead interactions.
- The Caroli formula and interface transmission formulas are recovered as special cases.
- An explicit formula for one-dimensional interface setups is derived.
Conclusions:
- The new formula provides a more comprehensive approach to calculating transmission coefficients.
- It offers a unified framework for analyzing heat and electrical transport.
- The derived formulas are applicable to various interface and ballistic transport scenarios.
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