We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.

中文翻译：

---

多体均场极限中Landau–Pekar方程的推导

我们认为Fröhlich哈密顿量处于平均场极限，其中许多玻色子粒子弱耦合到​​量化的声子场。对于大粒子数和适当小的耦合，我们表明系统的动力学近似由Landau–Pekar方程描述。这些描述了与经典极化场相互作用的玻色-爱因斯坦凝聚物，其动力学受凝聚物影响，即，粒子在时间演化过程中产生的声子的后反应处于领先地位。