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Quantum corrections to plasma kinetic equations: A deformation approach
João P S Bizarro1, João Cortes1, R Vilela Mendes2
1Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal.
Physical Review. E
|August 16, 2020
Summary
This study introduces a new method for quantum kinetic equations by deforming classical phase-space algebra. This approach offers quantum corrections for Vlasov-Poisson, Vlasov-Maxwell, and Boltzmann equations in quantum plasmas.
Area of Science:
- Plasma Physics
- Quantum Mechanics
- Condensed Matter Physics
Background:
- Classical kinetic equations are limited in describing quantum systems due to non-commuting variables.
- Quantum effects become significant in dense plasmas and nanostructures where de Broglie wavelength approaches interparticle distance.
Purpose of the Study:
- To develop a direct phase-space formulation for quantum kinetic equations.
- To derive quantum corrections for established kinetic equations like Vlasov-Poisson, Vlasov-Maxwell, and Boltzmann.
Main Methods:
- Modifying the classical Poisson algebra into a deformed algebra for quantum mechanics in phase space.
- Applying this deformed algebra to derive quantum versions of kinetic equations.
Main Results:
- Successfully derived quantum corrections for Vlasov-Poisson, Vlasov-Maxwell, and Boltzmann equations.
- Demonstrated a direct phase-space approach to quantum kinetic theory.
Conclusions:
- The deformed algebra approach provides a direct pathway to quantum kinetic equations.
- This method offers a novel way to incorporate quantum effects into the study of many-body systems.
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