The non-equilibrium dynamics of the excitonic insulator order parameter in the excitonic insulator phase of the Falicov–Kimball model excited by ultrashort laser pulse is studied. The Keldysh–Schwinger functional integral method with the saddle point approximation is employed. The numerical solution for the order parameter obtained from the saddle point equation is found to exhibit oscillatory behaviors, whose frequencies are consistent with the energy gap of the excitonic insulator. The fluctuations of the order parameter around the saddle point are identified with the collective modes in non-equilibrium states, and their Green’s functions are explicitly found in terms of the saddle point solution. Also, the interaction vertices responsible for the decay of the non-equilibrium order parameter is found, and the lowest order contribution for the decay process is expressed in terms of the vertices and the Green’s functions of the non-equilibrium collective modes. In the presence of a particular electron–phonon interaction, a hybrid mode of the excitonic order parameter and the phonon can be naturally defined in functional integral and its saddle point equation can be derived. It is shown that the saddle point solution with electron–phonon interaction is consistent with the experimental data and the existing theoretical result.

研究了由超短激光脉冲激发的 Falicov-Kimball 模型激子绝缘体相中激子绝缘体有序参数的非平衡动力学。采用带鞍点近似的 Keldysh-Schwinger 函数积分方法。发现从鞍点方程获得的阶次参数的数值解表现出振荡行为，其频率与激子绝缘体的能隙一致。鞍点附近阶参数的波动与非平衡状态下的集体模式相同，并且根据鞍点解明确找到了它们的格林函数。此外，还找到了导致非平衡顺序参数衰减的交互顶点，衰减过程的最低阶贡献用非平衡集体模式的顶点和格林函数表示。在存在特定的电子-声子相互作用的情况下，激子序参数和声子的混合模式可以自然地定义为泛函积分，并且可以导出其鞍点方程。结果表明，具有电子-声子相互作用的鞍点解与实验数据和现有理论结果一致。激子阶参数和声子的混合模式可以自然地定义在泛函积分中，并且可以导出其鞍点方程。结果表明，具有电子-声子相互作用的鞍点解与实验数据和现有理论结果一致。激子阶参数和声子的混合模式可以自然地定义在泛函积分中，并且可以导出其鞍点方程。结果表明，具有电子-声子相互作用的鞍点解与实验数据和现有理论结果一致。