Abstract
The de Broglie–Bohm pilot-wave theory provides an illuminating candidate solution to the philosophical problems that plague orthodox quantum theory. But the pilot-wave theory also has the potential to be of practical use to, for example, quantum chemists and condensed matter physicists who study many-body problems. In particular, the proprietary pilot-wave concept of the “conditional wave function” provides a novel perspective on and justification for a standard approach to many-body quantum systems in which the N-particle wave function is replaced by N single-particle wave functions. Moreover, this uniquely Bohmian “small entanglement approximation” (SEA) can be understood as the most basic level in a hierarchy of well-defined approximation schemes. Here we explain all of this theoretical background and then explore several of these approximation schemes (the SEA and beyond) numerically in the context of a simple toy model system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Goldstein, S.: Bohmian mechanics. In: Zalta, E.N. (ed.), The Stanford Encyclopedia of Philosophy, Fall 2021 edn. https://plato.stanford.edu/archives/fall2021/entries/qm-bohm/
Bell, J.S.: On the impossible pilot wave. In: Speakable and Unspeakable in Quantum Mechanics, 2nd edn. Cambridge University Press, Cambridge (2004)
Gindensperger, E., Meier, C., Beswick, J.A.: Mixing quantum and classical dynamics using Bohmian trajectories. J. Chem. Phys. 113(21), 9369–72 (2000)
Prezhdo, O., Brooksby, C.: Quantum backreaction through the Bohmian particle. Phys. Rev. Lett. 86(15), 3215–9 (2001)
Gindensperger, E., Meier, C., Beswick, J.A.: Hybrid quantum/classical dynamics using Bohmian trajectories. Adv. Quantum Chem. 47, 331–346 (2004)
Oriols, X.: Quantum trajectory approach to time-dependent transport in mesoscopic systems with electron-electron interactions. PRL 98, 066803 (2007)
Elsayed, T.A., et al.: Entangled quantum dynamics of many-body systems using Bohmian trajectories. Sci. Rep. 8, 12704 (2018)
Struyve, W.: Semi-classical approximations based on Bohmian mechanics. Int. J. Mod. Phys. A 35, 2050070 (2020)
Deckert, D.-A., et al.: Comparison of the mean-field and Bohmian semi-classical approximations to the Rabi model. Int. J. Mod. Phys. B 35, 2150270 (2021)
Norsen, T.: Foundations of Quantum Mechanics. Springer, New York (2017)
Norsen, T.: The theory of (exclusively) local beables. Found. Phys. 40, 1858 (2010)
Norsen, T., Marian, D., Oriols, X.: Can the wave function in configuration space be replaced by single-particle wave functions in physical space? Synthese 192, 3125–3151 (2015)
Author information
Authors and Affiliations
Contributions
TN wrote the manuscript text, created and ran all simulations, and prepared all figures.
Corresponding author
Ethics declarations
Conflict of interest
The author has no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Norsen, T. A Pilot-Wave Approach to the Many-Body Problem: Beyond the Small Entanglement Approximation. Found Phys 52, 103 (2022). https://doi.org/10.1007/s10701-022-00621-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10701-022-00621-6