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.(c) 2015 Wiley Periodicals, Inc.

Mean-field evolution of fermionic mixed states / Benedikter, N; Jaksic, V; Porta, M; Saffirio, C; Schlein, B. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 69:12(2016), pp. 2250-2303. [10.1002/cpa.21598]

Mean-field evolution of fermionic mixed states

Porta M;
2016-01-01

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.(c) 2015 Wiley Periodicals, Inc.
2016
69
12
2250
2303
https://arxiv.org/abs/1411.0843
Benedikter, N; Jaksic, V; Porta, M; Saffirio, C; Schlein, B
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/122469
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