Properties of a finite fully spin-polarized free homogeneous one-dimensional electron gas

Orion Ciftja

doi:10.1063/1.4907104

Abstract

The homogeneous electron gas model has been quite successful to predict the bulk properties of systems of electrons at various densities. In many occasions, a simplified free homogeneous electron gas model represents a powerful first approximation to a real system. Despite our considerable knowledge on the bulk properties of a homogeneous electron gas, advances in nanoscience and nanotechnology call for a greater effort to understand the opposite limit of small finite systems of electrons with size-dependent properties. In this work, we provide a detailed description of the properties of a finite fully spin-polarized (spinless) free homogeneous one-dimensional electron gas, the simplest of the free homogeneous electron gases. We derive exact analytical results for various quantities such as the one-particle density function, two-particle density function, one-particle density matrix, pair correlation function and energy of finite systems with an arbitrary number of electrons. The results obtained provide a detailed view on how various quantities corresponding to a finite system approach their bulk (thermodynamic limit) value.

Highlights

The theoretical description of Fermi systems, typically systems of electrons, has been the subject of many studies and has a long history.[1,2,3,4,5] Real systems of many electrons involve interactions and can be treated only by adopting models and approximations that attempt to solve the many-particle Schrödinger’s equation as accurately as possible
IV we describe in detail the calculations of the one-particle density matrix function and pair correlation function for a finite system with an arbitrary odd number (N = 1, 3, . . .) of electrons
In this work we studied the properties of a finite fully spin-polarized free 1DEG consisting of an arbitrary number of electrons

Summary

INTRODUCTION

The theoretical description of Fermi systems, typically systems of electrons, has been the subject of many studies and has a long history.[1,2,3,4,5] Real systems of many electrons involve interactions and can be treated only by adopting models and approximations that attempt to solve the many-particle Schrödinger’s equation as accurately as possible. In all other regards they manifest quantum behavior (they obey Pauli’s exclusion principle, and so on) From this perspective, a free electron gas model represents a quantum system of interaction-free electrons with the constrain that the particles should abide by the laws of quantum mechanics. In this work we derive exact analytic expressions for all relevant quantities (one-particle density matrix, pair correlation function, energy, etc) that correspond to a finite fully spin-polarized (spinless) free homogeneous 1DEG system of N electrons as a function of the arbitrary number of electrons. VII we draw some conclusions and present a brief summary of the results

GENERAL DEFINITIONS AND FORMALISM

ENERGY OF A FINITE SYSTEM

CONCLUSIONS