A Vlasov-Bohm approach to Quantum Mechanics for statistical systems
Quantum Physics
2025-12-15 v1
Abstract
Quantum mechanics is the most successful theory to describe microscopic phenomena. It was derived in different ways over the past 100 years by Heisenberg, Schr\"{o}dinger, and Feynman. At the same time, other interpretations have been suggested, including the Bohm-De Broglie interpretation and the so-called Bohmian mechanics. Here, we show that Bohmian mechanics, which utilizes the concept of the Bohm quantum potential, can also serve as a starting point for quantizing classical non-relativistic systems. By incorporating the Bohm quantum potential into the Vlasov framework, we obtain a mean-field theory that captures the corpuscular nature of matter, in agreement with quantum mechanics within the Random Phase Approximation (RPA).
Keywords
Cite
@article{arxiv.2512.11772,
title = {A Vlasov-Bohm approach to Quantum Mechanics for statistical systems},
author = {Pedro Luis Grande and Raul Carlos Fadanelli and Maarten Vos},
journal= {arXiv preprint arXiv:2512.11772},
year = {2025}
}