Linking boundary conditions for kinetic and hydrodynamic description of fermion gas

TL;DR

This paper develops an approximate analytical solution for the boundary slip problem in fermion gases under magnetic fields, linking kinetic and hydrodynamic descriptions with validated numerical results.

Contribution

It introduces a new approximate analytical method for boundary slip in fermion gases, connecting kinetic and hydrodynamic models more reliably.

Findings

The approximate solution accurately predicts slip length across models.

Numerical calculations confirm the method's reliability.

Application to Poiseuille flow demonstrates practical relevance.

Abstract

An approximate analytical solution of the boundary slip problem in magnetic field is obtained by using the general form of boundary conditions for the distribution function of fermions with the isotropic energy spectrum. Exact numerical calculations of the slip length for different models of angle-dependent specularity parameter and application of the results to the description of the Poiseuille flow demonstrate the reliability of the approximate solution for establishing a direct link between the hydrodynamic and the kinetic approaches to transport in bounded fermion systems.