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Eigenstates in the Many Interacting Worlds Approach: Focus on 2D Ground States

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Physics and the Nature of Reality

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 215))

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Abstract

The Many-Interacting-Worlds (MIW) approach to a quantum theory without wave functions proposed in [8] leads naturally to numerical integrators of the Schrödinger equation on comoving grids. As yet, little is known about concrete MIW models for more than one spatial dimension and/or more than one particle. In honour of Detlef Dürr, we report on a further development of the MIW approach to treat arbitrary degrees of freedom and provide a numerical proof of concept for ground states in 2d. The latter is part of a systematic numerical study [22] that includes also 1d ground and excited states. With this step towards the treatment of higher degrees of freedom we hope to stimulate their further study.

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Acknowledgements

We would like to thank M. Ghadimi and T. Gould for valuable discussions. Furthermore, D.-A.D. and H.H. would like to thank Griffith University for its hospitality, while M.J.W.H. and H.M.W. likewise thank the Ludwig Maximilian University. This work was partially funded by the Elite Network of Bavaria through the Junior Research Group “Interaction between Light and Matter” and by FQXi Grant FQXi-RFP-1519. Finally, since this is H.M.W.’s only contribution to this volume, I (H.M.W.) would like to take this opportunity to thank Detlef Dürr for being a source of wisdom and inspiration over many years, and for being a powerful friend and colleague for the unfortunately fewer years that I knew him personally.

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Authors and Affiliations

  1. Mathematisches Institut, Ludwig-Maximilians-Universität München, München, Germany

    Hannes Herrmann & Dirk-André Deckert

  2. Centre for Quantum Dynamics, Griffith University, Brisbane, QLD, 4111, Australia

    Michael J. W. Hall & Howard M. Wiseman

Authors
  1. Hannes Herrmann
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  2. Michael J. W. Hall
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  3. Howard M. Wiseman
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  4. Dirk-André Deckert
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Corresponding author

Correspondence to Dirk-André Deckert .

Editor information

Editors and Affiliations

  1. Department of Physics, University of Trieste, Trieste, Italy

    Angelo Bassi

  2. Department of Mathematics, Rutgers University, Piscataway, NJ, USA

    Sheldon Goldstein

  3. Fachbereich Mathematik, Eberhard Karls University of Tübingen, Tübingen, Baden-Württemberg, Germany

    Roderich Tumulka

  4. Dipartimento di Fisica, Università di Genova, Genova, Italy

    Nino Zanghì

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Herrmann, H., Hall, M.J.W., Wiseman, H.M., Deckert, DA. (2024). Eigenstates in the Many Interacting Worlds Approach: Focus on 2D Ground States. In: Bassi, A., Goldstein, S., Tumulka, R., Zanghì, N. (eds) Physics and the Nature of Reality. Fundamental Theories of Physics, vol 215. Springer, Cham. https://doi.org/10.1007/978-3-031-45434-9_10

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