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

6th International Workshop DICE2012 Spacetime – Matter – Quantum Mechanics: From the Planck Scale to Emergent Phenomena

物理学;力学

Dharma-Wardana, M.W.C.^1

National Research Council of Canada, Ottawa, K1A 0R6, Canada^1

关键词: De Broglie wavelength;    Density distributions;    Finite temperatures;    Hohenberg-Kohn theorem;    Macroscopic systems;    Pair distribution functions;    Pauli exclusion effects;    Quantum potentials;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/442/1/012030/pdf
DOI  :  10.1088/1742-6596/442/1/012030

学科分类：力学，机械学

来源: IOP

【 摘 要 】

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.