Electron relaxation in metals: Theory and exact analytical solutions

Details Electron relaxation in metals: Theory and exact analytical solutions Electron relaxation in metals: Theory and exact analytical solutions

2008-09-04

arxiv.org/abs/0809.0818v4

Phys. Rev. B 78, 174514 (2008)

Physics

Condensed Matter

Superconductivity

Citation list has been extended. The paper is submitted to the Physical Review B

Scientific paper

10.1103/PhysRevB.78.174514

The non-equilibrium dynamics of electrons is of a great experimental and theoretical value providing important microscopic parameters of the Coulomb and electron-phonon interactions in metals and other cold plasmas. Because of the mathematical complexity of collision integrals theories of electron relaxation often rely on the assumption that electrons are in a "quasi-equilibrium" (QE) with a time-dependent temperature, or on the numerical integration of the time-dependent Boltzmann equation. We transform the integral Boltzmann equation to a partial differential Schroedinger-like equation with imaginary time in a one-dimensional "coordinate" space reciprocal to energy which allows for exact analytical solutions in both cases of electron-electron and electron-phonon relaxation. The exact relaxation rates are compared with the QE relaxation rates at high and low temperatures.

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