The anisotropic distribution of the interacting electrons

TL;DR

This paper explores how electron-electron interactions in metals lead to anisotropic electron distributions in wave vector space, highlighting multiple possible solutions including isotropic and anisotropic configurations.

Contribution

It introduces the concept of multivalent distribution functions for interacting electrons, emphasizing the role of electron repulsion in creating anisotropic distributions.

Findings

Multiple solutions for electron distribution functions exist.

Electron repulsion can induce anisotropy in electron distributions.

Isotropic distribution is just one among many possible states.

Abstract

The distribution function for a system of interacting electrons in metals is multivalent in a certain region of wave vectors. One solution among many is isotropic. For other solutions the distribution of electrons over the wave vectors is anisotropic. In the simplest case, the anisotropy arises as a result of the repulsion between electrons in states with the wave vectors $\bf k$ and $-\hh\bf k$.