Applications of density matrix in the fractional quantum mechanics

TL;DR

This paper explores the application of density matrix methods to space fractional quantum mechanics, extending classical models and theories to fractional contexts, and deriving new results for electron gases and density functional theory.

Contribution

It introduces the use of density matrix techniques in fractional quantum mechanics, generalizing the Thomas-Fermi model and density functional theory to this new framework.

Findings

Derived quantum pressure of free electron gas in fractional space

Validated Hohenberg-Kohn theory within fractional quantum mechanics

Generalized density functional theory to fractional quantum systems

Abstract

The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, and obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theory in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics.