Longitudinal electric conductivity in a~quantum plasma with a~variable collision frequency in the~framework of the~Mermin approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 1, pp. 147-160
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In the framework of the Mermin approach, we obtain formulas for the longitudinal electric conductivity in a quantum collisional plasma with a collision frequency depending on the momentum. We use a kinetic equation in the momentum space in the relaxation approximation. We show that as the Planck constant tends to zero, the derived formula transforms into the corresponding formula for a classical plasma. We also show that as the frequency of collisions between plasma particles tends to zero (the plasma transforms into a collisionless plasma), the derived formula transforms into the well-known Klimontovich–Silin formula for the collisionless plasma. We show that if the collision frequency is constant, then the derived formula for the permittivity transforms into the well-known Mermin formula.
Keywords:
Klimontovich–Silin formula, Mermin approach, conductivity, quantum collisional plasma, Schrödinger equation.
@article{TMF_2014_178_1_a5,
author = {A. V. Latyshev and A. A. Yushkanov},
title = {Longitudinal electric conductivity in a~quantum plasma with a~variable collision frequency in the~framework of {the~Mermin} approach},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {147--160},
publisher = {mathdoc},
volume = {178},
number = {1},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2014_178_1_a5/}
}
TY - JOUR AU - A. V. Latyshev AU - A. A. Yushkanov TI - Longitudinal electric conductivity in a~quantum plasma with a~variable collision frequency in the~framework of the~Mermin approach JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2014 SP - 147 EP - 160 VL - 178 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2014_178_1_a5/ LA - ru ID - TMF_2014_178_1_a5 ER -
%0 Journal Article %A A. V. Latyshev %A A. A. Yushkanov %T Longitudinal electric conductivity in a~quantum plasma with a~variable collision frequency in the~framework of the~Mermin approach %J Teoretičeskaâ i matematičeskaâ fizika %D 2014 %P 147-160 %V 178 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2014_178_1_a5/ %G ru %F TMF_2014_178_1_a5
A. V. Latyshev; A. A. Yushkanov. Longitudinal electric conductivity in a~quantum plasma with a~variable collision frequency in the~framework of the~Mermin approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 1, pp. 147-160. http://geodesic.mathdoc.fr/item/TMF_2014_178_1_a5/