An equation on random variables and systems of fermions

TL;DR

This paper studies an equation modeling the evolution of fermion systems, providing well-posedness, scattering, and blow-up results across different geometries, and interprets these findings in the context of fermionic dynamics.

Contribution

It introduces an equation on random variables linked to fermion systems and establishes well-posedness, scattering, and blow-up results in various settings, offering new insights into fermionic evolution.

Findings

Well-posedness on spheres, tori, and Euclidean space

Scattering results for defocusing equations

Blow-up phenomena for focusing equations

Abstract

In this paper, we consider an equation on random variables which can be reduced to the equation which describes the evolution of systems of fermions. We give some results of well-posedness for this equation on the spheres and torus of dimension 2 and 3 and on the Euclidean space. We give results of scattering and blow-up on the Euclidean depending on if the equation is defocusing or focusing. We interpret the results in terms of the evolution of fermions.