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.
Mean-Field Evolution of Fermionic Mixed States / N. Benedikter, V. Jaksic, M. Porta, C. Saffirio, B. Schlein. - 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
N. Benedikter;
2016
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.File | Dimensione | Formato | |
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