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

TL;DR

This paper explores the foundational implications of density-functional theory (DFT) and classical mappings of quantum systems at finite temperatures, offering new insights into quantum correlations and the nature of macroscopic quantum states.

Contribution

It investigates the connection between DFT, classical models, and quantum correlations, revealing new perspectives on quantum foundations and the role of non-local effects.

Findings

Classical maps of quantum pair-distribution functions provide new insights into quantum correlations.

Finite-temperature classical models can mimic quantum effects like Pauli exclusion.

Macroscopic systems at low temperatures lack macroscopic cat states due to de Broglie wavelength considerations.

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 {\it without} the need for an n-body wavefunction \psi. DFT uses the one-body density distribution instead of \psi. 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 \to hybrid \to 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 {\it ad hoc} decoherence models.