标题： 准相对论共振中的量子冲击波 显示英文标题

标题： Quantum shockwave at the quasi-relativistic resonance

摘要： 冲击波是波动传播中剧烈的非线性畸变，已在流体波和电磁波中被报道，而这里我们揭示了即使在单个粒子的量子波函数中也会出现冲击波。 具体来说，我们分析了共振于准相对论粒子极限速度的电磁场，并发现强烈的纵向场可以在粒子波函数中撕裂出一个量子冲击波奇点，从而导致能量耗散。 此外，我们表明，由于石墨烯中的准相对论（狄拉克）电子具有两个原因，这种效应尤为显著。 一方面，由于有效电子质量较小，我们能够在非常小的场强下获得单粒子冲击波；另一方面，通过利用石墨烯中的高电子密度，我们可以获得较大的多粒子冲击波耗散。 虽然单粒子冲击波可以通过高分辨率显微镜定位冲击波奇点来最轻松地观测到，但多粒子耗散则会表现为共振电磁场的快速衰减。 显示英文摘要

摘要： Shockwaves are violent nonlinear distortions of wave motion which have been reported in fluid waves and electromagnetic waves, while here we reveal that a shockwave can occur even in the quantum wave function of a single particle. Specifically, we analyze the electromagnetic field travelling on resonance with the limiting velocity of the quasi-relativistic particle, and reveal that a strong longitudinal field can rip up a quantum shockwave singularity in the particle wave function, leading to energy dissipation. Moreover, we show that this effect is particularly strong for quasi-relativistic (Dirac) electrons in graphene for two reasons. On one hand, we obtain the single-particle shockwave at very small fields due to the small effective electron mass, and on the other hand we can obtain large dissipation in the many-particle shockwave by using the large electron density in graphene. While the single-particle shockwave can be most easily observed by locating the shockwave singularity with a high-resolution microscopy, the many-particle dissipation would be simply observed as a rapid decay of our resonant electromagnetic field.