Mean‐Field Evolution of Fermionic Mixed States |
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| Authors: | Niels Benedikter Vojkan Jak?i? Marcello Porta Chiara Saffirio Benjamin Schlein |
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| Institution: | 1. Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark;2. Mathematics and Statistics Department, McGill University, Montreal, QC, Canada;3. Mathematics Department, University of Zürich, Zürich, Switzerland |
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| 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.© 2015 Wiley Periodicals, Inc. |
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