Abstract:
This is a short review of the theory of chaos in Bohmian quantum mechanics based on our series of works in this field. Our first result is the development of a generic theoretical mechanism responsible for the generation of chaos in an arbitrary Bohmian system (in 2 and 3 dimensions). This mechanism allows us to explore the effect of chaos on Bohmian trajectories and study in detail (both analytically and numerically) the different kinds of Bohmian trajectories where, in general, chaos and order coexist. Finally, we explore the effect of quantum entanglement on the evolution of the Bohmian trajectories and study chaos and ergodicity in qubit systems which are of great theoretical and practical interest. We find that the chaotic trajectories are also ergodic, i. e., they give the same final distribution of their points after a long time regardless of their initial conditions. In the case of strong entanglement most trajectories are chaotic and ergodic and an arbitrary initial distribution of particles will tend to Born’s rule over the course of time. On the other hand, in the case of weak entanglement the distribution of Born’s rule is dominated by ordered trajectories and consequently an arbitrary initial configuration of particles will not tend, in general, to Born’s rule unless it is initially satisfied. Our results shed light on a fundamental problem in Bohmian mechanics, namely, whether there is a dynamical approximation of Born’s rule by an arbitrary initial distribution of Bohmian particles.
Keywords:
chaos, Bohmian mechanics, entanglement.
Funding agency
This research was conducted in the framework of the program of the RCAAM of Athens “Study
of the dynamical evolution of the entanglement and coherence in quantum systems”.
\Bibitem{ConTze20}
\by George Contopoulos, Athanasios C. Tzemos
\paper Chaos in Bohmian Quantum Mechanics: A Short Review
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 5
\pages 476--495
\mathnet{http://mi.mathnet.ru/rcd1078}
\crossref{https://doi.org/10.1134/S1560354720050056}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4155406}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000573268200005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85091653406}
Linking options:
https://www.mathnet.ru/eng/rcd1078
https://www.mathnet.ru/eng/rcd/v25/i5/p476
This publication is cited in the following 13 articles:
Henrique Santos Lima, Matheus M. A. Paixão, Constantino Tsallis, “de Broglie–Bohm analysis of a nonlinear membrane: From quantum to classical chaos”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34:2 (2024)
A.C. Tzemos, G. Contopoulos, “A comparison between classical and Bohmian quantum chaos”, Chaos, Solitons & Fractals, 188 (2024), 115524
George Contopoulos, Athanasios C. Tzemos, “Classical and Bohmian Trajectories in Integrable and Nonintegrable Systems”, Particles, 7:4 (2024), 1062
Athanasios C. Tzemos, Springer Proceedings in Complexity, Chaos, Fractals and Complexity, 2023, 71
Athanasios C. Tzemos, George Contopoulos, “Order, Chaos and Born's Distribution of Bohmian Particles”, Particles, 6:4 (2023), 923
A C Tzemos, G Contopoulos, “Chaos and ergodicity in a partially integrable 3d Bohmian system: a comparison with 2d systems”, Phys. Scr., 98:6 (2023), 065223
Martin Bojowald, Ari Gluckman, “Chaos in a tunneling universe”, J. Cosmol. Astropart. Phys., 2023:11 (2023), 052
Héctor M. Moya-Cessa, Felipe A. Asenjo, Sergio A. Hojman, Francisco Soto-Eguibar, “Two-mode squeezed state generation using the Bohm potential”, Mod. Phys. Lett. B, 36:09 (2022)
Martin Bojowald, Pip Petersen, “Tunneling dynamics of an oscillating universe model”, J. Cosmol. Astropart. Phys., 2022:05 (2022), 007
Athanasios C. Tzemos, George Contopoulos, “Bohmian Chaos in Multinodal Bound States”, Found Phys, 52:4 (2022)
A. Drezet, “Justifying Born's rule Pα=|Ψα|2 using deterministic chaos, decoherence, and the de Broglie-Bohm quantum theory”, Entropy, 23:11 (2021), 1371
D. Li, J. Duan, L. Lin, A. Zhang, “Bohmian trajectories of the time-oscillating Schrodinger equations”, Chaos, 31:10 (2021), 101101
A. C. Tzemos, G. Contopoulos, “The role of chaotic and ordered trajectories in establishing Born's rule”, Phys. Scr., 96:6 (2021), 065209