We consider the dynamics of interacting fermionic systems, in the mean-field regime. As the number of particles goes to infinity, the evolution of the system is expected to be well approximated by the time-dependent Hartree-Fock equation, a well-known example of effective evolution equation. We review some rigorous results about the validity of this approximation. We start by discussing the case of systems of particles interacting via bounded interaction potentials, at zero and at positive temperature. Under the assumption that a suitable semiclassical structure is propagated in time along the flow of the Hartree-Fock equation, the result can be extended to the case of Coulomb interactions.

Mean field dynamics of interacting fermionic systems / Porta, M. - 717:(2018), pp. 13-30. ((Intervento presentato al convegno 13th Conference on Mathematical Results in Quantum Physics (QMATH) tenutosi a GeorgiaTech, Atlanta nel 8 Ottobre 2016 - 11 Ottobre 2016 [10.1090/conm/717/14438].

Mean field dynamics of interacting fermionic systems

Porta M
2018-01-01

Abstract

We consider the dynamics of interacting fermionic systems, in the mean-field regime. As the number of particles goes to infinity, the evolution of the system is expected to be well approximated by the time-dependent Hartree-Fock equation, a well-known example of effective evolution equation. We review some rigorous results about the validity of this approximation. We start by discussing the case of systems of particles interacting via bounded interaction potentials, at zero and at positive temperature. Under the assumption that a suitable semiclassical structure is propagated in time along the flow of the Hartree-Fock equation, the result can be extended to the case of Coulomb interactions.
Mathematical Problems in Quantum Physics
717
13
30
978-1-4704-3681-0
978-1-4704-4939-1
http://www.ams.org/books/conm/717/
American Mathematical Society
Porta, M
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/122457
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact