论文标题
高密度状态下扩展费米气体的有效动力学
Effective Dynamics of Extended Fermi Gases in the High-Density Regime
论文作者
论文摘要
我们研究了任意大域中三维中多体费米气体的量子演化。我们认为这两个粒子具有非依赖性和相对论分散体。我们将重点放在半经典缩放中的高密度制度上，并考虑一类描述零温度状态的初始数据。在非权利论的情况下，我们证明，随着密度为无穷大，在短的宏观时期，降低的一颗粒子密度矩阵的多体演化会收敛到时间依赖性的hartree方程的溶液。在相对论分散的情况下，我们在所有宏观时期都显示了多体演变与相对论的哈特里方程的融合。关于以前的工作，收敛速率不取决于粒子总数，而仅取决于密度：特别是，我们的结果使我们能够研究广泛的多体费米气体的量子动力学。
We study the quantum evolution of many-body Fermi gases in three dimensions, in arbitrarily large domains. We consider both particles with non-relativistic and with relativistic dispersion. We focus on the high-density regime, in the semiclassical scaling, and we consider a class of initial data describing zero-temperature states. In the non-relativistic case we prove that, as the density goes to infinity, the many-body evolution of the reduced one-particle density matrix converges to the solution of the time-dependent Hartree equation, for short macroscopic times. In the case of relativistic dispersion, we show convergence of the many-body evolution to the relativistic Hartree equation for all macroscopic times. With respect to previous work, the rate of convergence does not depend on the total number of particles, but only on the density: in particular, our result allows us to study the quantum dynamics of extensive many-body Fermi gases.
