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Quantum kinetic equation for the Wigner function and reduction to the Boltzmann transport equation under discrete
1Institute of Applied Physics, University of Tsukuba and 1-1-1 Tennoudai, Tsukuba, Ibaraki 305-8573, Japan.
Physical Review. E
|August 20, 2021
Summary
This study presents a new quantum kinetic equation for Wigner functions with discrete impurities, correcting inconsistencies in prior methods. The derived Boltzmann transport equation accurately models impurity scattering and potential fluctuations.
Area of Science:
- Quantum kinetic theory
- Condensed matter physics
- Semiconductor transport
Background:
- Wigner function formalism is crucial for describing quantum transport.
- Impurity scattering significantly impacts electronic properties in materials.
- Existing models often oversimplify or inconsistently treat impurity scattering.
Purpose of the Study:
- To derive a consistent quantum kinetic equation for Wigner functions considering discrete impurities.
- To address inconsistencies in the conventional treatment of impurity scattering.
- To develop a Boltzmann transport equation applicable to discrete impurity potentials.
Main Methods:
- Derivation from the quantum Liouville equation.
- Separation of Coulomb potential into long- and short-range components.
- Self-consistent coupling with Poisson's equation.
Main Results:
- A unified derivation of the collision integral and drift term.
- Identification of inconsistencies and double-counting in previous Wigner function treatments of impurity scattering.
- Derivation of the Boltzmann transport equation without assuming random impurity distribution.
Conclusions:
- The new quantum kinetic equation provides a more accurate description of electron transport in the presence of discrete impurities.
- The derived Boltzmann transport equation is suitable for modeling phenomena like potential fluctuations caused by discrete impurities.
- This work offers a rigorous framework for understanding quantum transport in disordered systems.
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