The quantum acoustic framework has recently emerged as a nonperturbative, coherent approach to electron–lattice interactions, uncovering rich physics often obscured by perturbative methods with incoherent scattering events. Here, we model the strongly coupled dynamics of electrons and acoustic lattice vibrations within this framework, representing lattice vibrations as coherent states and electrons as quantum wave packets, in a manner distinctively different from tight-binding or discrete hopping-based approaches. We derive and numerically implement electron backaction on the lattice, providing both visual and quantitative insights into electron wave packet evolution and the formation of acoustic polarons. We investigate polaron binding energies across varying material parameters and compute key observables—including mean square displacement, kinetic energy, potential energy, and vibrational energy—over time. Our findings reveal the conditions that favor polaron formation, which is enhanced by low temperatures, high deformation potential constants, slow sound velocities, and high effective masses. Additionally, we explore the impact of external electric and magnetic fields, showing that while polaron formation remains robust under moderate fields, it is weakly suppressed at higher field strengths. These results deepen our understanding of polaron dynamics and pave the way for future studies into nontrivial transport behavior in quantum materials.

中文翻译：

---

量子声学中的极化子灾难

量子声学框架最近作为一种非扰动、相干的电子-晶格相互作用方法出现，揭示了丰富的物理学，这些物理学经常被具有非相干散射事件的微扰方法所掩盖。在这里，我们模拟了该框架内电子和声晶格振动的强耦合动力学，将晶格振动表示为相干态，将电子表示为量子波包，其方式与紧密绑定或基于离散跳跃的方法截然不同。我们推导并数值地实现了晶格上的电子反作用，为电子波包的演化和声学极化子的形成提供了视觉和定量的见解。我们研究了不同材料参数中的极化子结合能，并计算了随时间变化的关键可观察物，包括均方位移、动能、势能和振动能。我们的研究结果揭示了有利于极化子形成的条件，低温、高变形电位常数、低声速和高有效质量增强了极化子的形成。此外，我们探讨了外部电场和磁场的影响，表明虽然极化子的形成在中等磁场下保持稳健，但在较高的场强下受到微弱的抑制。这些结果加深了我们对极化子动力学的理解，并为未来研究量子材料中非平凡的输运行为铺平了道路。