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.
| File | Dimensione | Formato | |
|---|---|---|---|
|
978-981-99-5894-8.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
9.88 MB
Formato
Adobe PDF
|
9.88 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
|
2207.07939v1.pdf
accesso aperto
Tipologia:
Pre-print (manoscritto inviato all'editore)
Dimensione
175.82 kB
Formato
Adobe PDF
|
175.82 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
