论文标题
Landau-pekar方程和量子波动的强烈耦合极性的动力学
Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron
论文作者
论文摘要
我们认为fröhlichHamiltonian具有较大的耦合常数$α$。对于具有连贯的声子字段的Pekar产品形式的初始数据，并且通过电子最小化相应能量的电子形式，我们提供了进化的标准近似，有效期为$α^2 $的阶段。近似是根据pekar乘积状态给出的，该状态通过Landau-pekar方程进化出来，该方程通过bogoliubov动力学纠正，考虑到量子波动。这使我们能够证明Landau-Pekar方程大致描述了fröhlich动力学下电子和单次降低密度矩阵的演变，直到订单$α^2 $的时间。
We consider the Fröhlich Hamiltonian with large coupling constant $α$. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolution, valid up to times of order $α^2$. The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order $α^2$.
