Mean-Field Evolution of Fermionic Mixed States

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.

在本文中，我们研究了平均场区域内费米子混合态的动力学。我们考虑接近准自由态的初始态，并证明在对初始数据和多体相互作用的适当假设下，此类初始数据的量子演化可由一个合适的准自由态很好地近似。特别地，我们证明了当粒子数趋于无穷时，约化单粒子密度矩阵的演化收敛于含时哈特里 - 福克方程的解。我们的结果对所有时间都成立，并对多体动力学向哈特里 - 福克演化的收敛速率给出了有效的估计。（c）2015威利期刊公司