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Mean‐Field Evolution of Fermionic Mixed States
Author(s) -
Benedikter Niels,
Jakšić Vojkan,
Porta Marcello,
Saffirio Chiara,
Schlein Benjamin
Publication year - 2016
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21598
Subject(s) - mathematics , density matrix , convergence (economics) , fock space , time evolution , matrix (chemical analysis) , infinity , field (mathematics) , state (computer science) , mean field theory , statistical physics , quantum , mathematical physics , quantum mechanics , physics , mathematical analysis , pure mathematics , materials science , algorithm , economics , composite material , economic growth
In this paper we study the dynamics of fermionic mixed states in the mean‐field regime. We consider initial states that are close to quasi‐free states and prove that, under suitable assumptions on the initial data and on the many‐body interaction, the quantum evolution of such initial data is well approximated by a suitable quasi‐free state. In particular, we prove that the evolution of the reduced one‐particle density matrix converges, as the number of particles goes to infinity, to the solution of the time‐dependent Hartree‐Fock equation. Our result holds for all times and gives effective estimates on the rate of convergence of the many‐body dynamics towards the Hartree‐Fock evolution.© 2015 Wiley Periodicals, Inc.