一维电子系统中的波动力学：由population inversion驱动的密度振荡
Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion
摘要：
我们探讨了一维电子系统中由局部猝灭引起的密度脉冲的动力学。光谱曲率导致波的“翻转”（粒子数反转）。我们表明，超过这个时间的密度分布发展强烈的振荡周期远大于费米波长。本文首先通过直接量子模拟和维格纳函数演化的半经典分析，研究了自由费米子的这种效应。然后，我们证明，振荡的周期是正确地再现流体动力学理论与适当的色散项。最后，我们探讨了不同类型的电子-电子相互作用对这种现象的影响。我们表明，足够强相互作用[ $U(r)\gg 1/mr^2$其中$m$是费米子质量和$r$相关的空间尺度]确定的流体动力学方程中的主导色散项。流体动力学理论揭示了密度演化对相互作用和密度扰动的相对符号的重要依赖性。
英文摘要：
We explore dynamics of a density pulse induced by a local quench in a one-dimensional electron system. The spectral curvature leads to an "overturn" (population inversion) of the wave. We show that beyond this time the density profile develops strong oscillations with a period much larger than the Fermi wave length. The effect is studied first for the case of free fermions by means of direct quantum simulations and via semiclassical analysis of the evolution of Wigner function. We demonstrate then that the period of oscillations is correctly reproduced by a hydrodynamic theory with an appropriate dispersive term. Finally, we explore the effect of different types of electron-electron interaction on the phenomenon. We show that sufficiently strong interaction [$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatial scale] determines the dominant dispersive term in the hydrodynamic equations. Hydrodynamic theory reveals crucial dependence of the density evolution on the relative sign of the interaction and the density perturbation.
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