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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.

Two Comments on the Derivation of the Time-Dependent Hartree-Fock Equation / N. Benedikter, D. Desio (SPRINGER INDAM SERIES). - In: Quantum Mathematics I / [a cura di] Michele Correggi, Marco Falconi. - [s.l] : Springer, 2023 Dec 01. - ISBN 978-981-99-5893-1. - pp. 319-333 (( convegno INdAM Meeting: Quantum Mathematics Workshop tenutosi a Milano nel 2022 [10.1007/978-981-99-5894-8_13].

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

N. Benedikter
Primo
;
2023

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.
No
English
Mathematical Physics; Mathematical Physics; Mathematics - Mathematical Physics; 81V70, 82B10, 81Q10, 35P05
Settore MAT/07 - Fisica Matematica
Capitolo o Saggio
Esperti anonimi
Pubblicazione scientifica
   The Mathematics of Interacting Fermions (FermiMath)
   FermiMath
   EUROPEAN COMMISSION
   101040991
Quantum Mathematics I
Michele Correggi, Marco Falconi
Springer
1-dic-2023
319
333
15
978-981-99-5893-1
978-981-99-5894-8
57
Volume a diffusione internazionale
No
INdAM Meeting: Quantum Mathematics Workshop
Milano
2022
arxiv
2-s2.0-85179338712
Aderisco
N. Benedikter, D. Desio
Book Part (author)
partially_open
268
Two Comments on the Derivation of the Time-Dependent Hartree-Fock Equation / N. Benedikter, D. Desio (SPRINGER INDAM SERIES). - In: Quantum Mathematics I / [a cura di] Michele Correggi, Marco Falconi. - [s.l] : Springer, 2023 Dec 01. - ISBN 978-981-99-5893-1. - pp. 319-333 (( convegno INdAM Meeting: Quantum Mathematics Workshop tenutosi a Milano nel 2022 [10.1007/978-981-99-5894-8_13].
info:eu-repo/semantics/bookPart
2
Prodotti della ricerca::03 - Contributo in volume
03 - Contributo in volume
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1039140
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