We extend the description of the non-equilibrium Gross-Pitaevskii equation for microcavity polaritons by including not only the kinetics of the non-resonantly pumped exciton reservoir but also that of the collective excitations - called bogolons - above the condensate. Quasi-equilibrium Hartree-Fock-Bogoliubov-Popov self-energies are used to describe the condensate and the bogolons. With non-equilibrium Green functions, the quantum Boltzmann equation of the bogolons in a frame moving with the condensate, together with the coupled Gross-Pitaevskii equation can be derived. The resulting scattering rates contain vertex corrections in form of symmetrized products of the u,v pairing functions of all involved scattering states. Corresponding results have been derived for ultra-cold atoms by Griffin et al. Furthermore, we show that the results of the quantum kinetics also determine the luminescence spectrum including the ghost branch. The kinetics is solved numerically, the resulting condensate, the bogolon distribution, and the luminescence are calculated temporally and spatially resolved after the switch-on of a non-resonant pump beam with a Gaussian profile. It is studied in detail to which extent the bogolons approach a local thermal equilibrium.

中文翻译：

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非平衡极化子冷凝物激发的动力学和发光

我们不仅包括微谐振子激子的非平衡Gross-Pitaevskii方程的描述，而且还包括凝结液上方非共振泵激激子储层的动力学，也包括集体激发（称为bogolons）的动力学。准平衡Hartree-Fock-Bogoliubov-Popov自能用于描述冷凝水和Bogolon。使用非平衡格林函数，可以导出与冷凝物一起移动的框架中的双子座的量子玻尔兹曼方程，以及耦合的Gross-Pitaevskii方程。产生的散射率包含所有涉及散射状态的u，v配对函数的对称乘积形式的顶点校正。Griffin等人已经得出了超冷原子的相应结果。此外，我们表明，量子动力学的结果还决定了包括幻影分支在内的发光光谱。数值求解动力学，在打开具有高斯分布的非共振泵浦光束后，在时间和空间上解析得到的冷凝物，bogolon分布和发光。对其进行了详细研究，在多大程度上Bogolons达到了局部热平衡。