Density-functional theory, finite-temperature classical maps, and their implications for foundational studies of quantum systems

M W C Dharma-Wardana

doi:10.1088/1742-6596/442/1/012030

Abstract

The advent of the Hohenberg-Kohn theorem in 1964, its extension to finite-T, Kohn-Sham theory, and relativistic extensions provide the well-established formalism of density-functional theory (DFT). This theory enables the calculation of all static properties of quantum systems without the need for an n-body wavefunction ψ. DFT uses the one-body density distribution instead of ψ. The more recent time-dependent formulations of DFT attempt to describe the time evolution of quantum systems without using the time-dependent wavefunction. Although DFT has become the standard tool of condensed-matter computational quantum mechanics, its foundational implications have remained largely unexplored. While all systems require quantum mechanics (QM) at T=0, the pair-distribution functions (PDFs) of such quantum systems have been accurately mapped into classical models at effective finite-T, and using suitable non-local quantum potentials (e.g., to mimic Pauli exclusion effects). These approaches shed light on the quantum → hybrid → classical models, and provide a new way of looking at the existence of non- local correlations without appealing to Bell's theorem. They also provide insights regarding Bohmian mechanics. Furthermore, macroscopic systems even at 1 Kelvin have de Broglie wavelengths in the micro-femtometer range, thereby eliminating macroscopic cat states, and avoiding the need for ad hoc decoherence models.

Highlights

In 1964, Hohenberg and Kohn [1] proved a theorem asserting that the ground- state properties of a stationary, non-relativistic system can be calculated from a variational principle involving only the one-body density n(r) of the system, without recourse to the Schrodinger equation and its wavefunction
The method, re-written in the form of the Kohn-Sham theory has become the preferred method in computational quantum mechanics (QM)
In the following presentation we look at density-functional theory (DFT) and compare it with relevant aspects of Bohmian mechanics, treatment of hybrid systems within DFT, as well as classical representations inspired by DFT ideas

Summary

Introduction

In 1964, Hohenberg and Kohn [1] proved a theorem asserting that the ground- state properties of a stationary, non-relativistic system can be calculated from a variational principle involving only the one-body density n(r) of the system, without recourse to the Schrodinger equation and its wavefunction. It became clear that all thermodynamic properties of n-particle quantum systems, entangled, interacting, or not, could be calculated without recourse to the n-body wavefunction. It is of interest at this stage to examine Bohmian mechanics, where the Schrodinger many-particle wavefunction ψ(x1, · · · xn) is used to construct a non-linear equation of motion containing the external potential as well as a quantum potential Q(x1, · · · xn).

Results

Conclusion