Describing the dynamics of many-electron quantum systems is crucial for
applications such as predicting electronic structures in quantum chemistry, the
properties of condensed matter systems, and the behaviors of complex materials.
However, the real-time evolution of non-equilibrium quantum electronic systems
poses a significant challenge for theoretical and computational approaches, due
to the system's exploration of a vast configuration space. This work introduces
a variational approach for fermionic time-dependent wave functions, surpassing
mean-field approximations by capturing many-body correlations. The proposed
methodology involves parameterizing the time-evolving quantum state, enabling
the approximation of the state's evolution. To account for electron
correlations, we employ time-dependent Jastrow factors and backflow
transformations. We also show that we can incorporate neural networks to
parameterize these functions. The time-dependent variational Monte Carlo
technique is employed to efficiently compute the optimal time-dependent
parameters. The approach is demonstrated in three distinct systems: the
solvable harmonic interaction model, the dynamics of a diatomic molecule in
intense laser fields, and a quenched quantum dot. In all cases, we show clear
signatures of many-body correlations in the dynamics not captured by mean-field
methods. The results showcase the ability of our variational approach to
accurately capture the time evolution of quantum states, providing insight into
the quantum dynamics of interacting electronic systems, beyond the capabilities
of mean-field.

这项研究介绍了一种变分方法，用于描述多电子量子系统的时间演化，在捕捉多体相关性方面超越平均场近似，通过参数化时间演化的量子态来近似状态的演化，并利用时间相关的 Jastrow 因子和反流变换来考虑电子的相关性。研究还展示了使用神经网络来参数化这些函数的方法，并通过三个不同的系统进行了验证。结果显示我们的变分方法能够准确捕捉量子态的时间演化，揭示了相互作用电子系统的量子动力学，超越了平均场方法的能力。