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Mean-field evolution of fermionic mixed states


Benedikter, Niels; Jakšić, Vojkan; Porta, Marcello; Saffirio, Chiara; Schlein, Benjamin (2016). Mean-field evolution of fermionic mixed states. Communications on Pure and Applied Mathematics, 69(12):2250-2303.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2016
Deposited On:03 Feb 2016 08:15
Last Modified:08 Dec 2017 16:52
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0010-3640
Publisher DOI:https://doi.org/10.1002/cpa.21598

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