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Two Comments on the Derivation of the Time-Dependent Hartree–Fock Equation

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Quantum Mathematics I (INdAM 2022)

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Abstract

We revisit the derivation of the time-dependent Hartree–Fock equation for interacting fermions in a regime coupling a mean-field and a semiclassical scaling, contributing two comments to the result obtained in 2014 by Benedikter, Porta, and Schlein. First, the derivation holds in arbitrary space dimension. Second, by using an explicit formula for the unitary implementation of particle-hole transformations, we cast the proof in a form similar to the coherent state method of Rodnianski and Schlein for bosons.

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Acknowledgements

NB has been supported by Gruppo Nazionale per la Fisica Matematica (GNFM) in Italy and the European Research Council (ERC) through the Starting Grant FermiMath, grant agreement nr. 101040991. The authors acknowledge the support of Istituto Nazionale di Alta Matematica “F. Severi” through the Intensive Period “INdAM Quantum Meetings (IQM22)”. The authors do not have any conflicts of interest to disclose.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli studi di Milano, Milano, Italy

    Niels Benedikter

  2. Dipartimento di Fisica, Università degli studi di Milano, Milano, Italy

    Davide Desio

Authors
  1. Niels Benedikter
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  2. Davide Desio
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Correspondence to Niels Benedikter .

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Editors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Michele Correggi

  2. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Marco Falconi

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Benedikter, N., Desio, D. (2023). Two Comments on the Derivation of the Time-Dependent Hartree–Fock Equation. In: Correggi, M., Falconi, M. (eds) Quantum Mathematics I. INdAM 2022. Springer INdAM Series, vol 57. Springer, Singapore. https://doi.org/10.1007/978-981-99-5894-8_13

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