Many-body theories for negative kinetic energy systems

TL;DR

This paper develops many-body theoretical frameworks for systems with particles possessing negative kinetic energy, extending existing theories like Thomas-Fermi and Hartree-Fock to negative temperature regimes.

Contribution

It introduces the first comprehensive many-body theories for negative kinetic energy systems, including adaptations of established models for negative temperature states.

Findings

Formulation of Thomas-Fermi, Hohenberg-Kohn, Kohn-Sham, and Hartree-Fock theories for NKE systems.

Extension of these theories to both zero and finite negative temperatures.

Proposal of an experiment to verify NKE electrons in tunneling phenomena.

Abstract

In the author's previous works, it is derived from the Dirac equation that particles can have negative kinetic energy (NKE) solutions, and they should be treated on an equal footing as the positive kinetic energy (PKE) solutions. More than one NKE particles can make up a stable system by means of interactions between them and such a system has necessarily negative temperature. Thus, many-body theories for NKE systems are desirable. In this work, the many-body theories for NKE systems are presented. They are Thomas-Fermi method, Hohenberg-Kohn theorem, Khon-Sham self-consistent equations, and Hartree-Fock self-consistent equations. They are established imitating the theories for PKE systems. In each theory, the formalism of both zero temperature and finite negative temperature are given. In order to verify that tunneling electrons are of NKE and real momentum, an experiment scenario is suggested that lets PKE electrons collide with tunneling electrons.