Bloch电子在均匀电场中的时间图像
The temporal picture for Bloch electron dynamics in homogeneous electric fields
AI总结：
研究了在均匀电场中布洛赫电子的动力学，揭示了电子从真实质量到有效质量的转变过程，以及其在超强电场下的行为特性。
摘要：
为在任意时间依赖的均匀电场中加速的Bloch电子发展了瞬态图像。分析的时间序列包括电子注入后的瞬间，随后是电子波数的小变化远离初始注入所需的时间，最终是经过许多布洛赫周期的最终时间演化。通过薛定谔方程的性质研究时间依赖行为。电场通过矢量势规范描述，且使用布洛赫、电场依赖的哈密顿量的瞬时本征态作为基态来描述电场中的布洛赫动力学。对于每个考虑的时间序列，建立并比较讨论薛定谔方程的解。在常数电场的一阶特殊情况下，获得动量期望值；由此得出的速度是最近文献中讨论的自然Zitterbewegung-like行为的场依赖性推广。早期时间和长时间极限下的动量期望值及其时间导数表明，在电场影响下电子通过带结构加速时，初始带注入后的阻力从真实质量动态变化到有效质量动态。这种从自由质量电子早期注入到有效质量电子的惯性变化是由于真实质量电子在晶体状态中“ dressing-up”成为有效质量电子的结果。讨论这种时间“ dressing”行为的后果，以考虑超强电场下布洛赫电子的一般动力学。
英文摘要：
The transient picture for a Bloch electron accelerating in an arbitrarily time-dependent homogeneous electric field is developed. The temporal sequence for the analysis includes the instant after electron injection, followed by the time required for a small change in electron wavenumber away from initial injection, leading to the final time evolution over many Bloch periods. The time-dependent behavior is studied using the properties of the Schrödinger equation. The electric field is described through the vector potential gauge, and the instantaneous eigenstates of the Bloch, electric-field-dependent Hamiltonian are used as basis states in describing the Bloch dynamics in the electric field. For each temporal sequence considered, the solution to the Schrödinger equation is established and comparatively discussed. The expectation value of the momentum is obtained for the special case of first order in a constant electric field; the resulting velocity derived is a field-dependent generalization of the natural Zitterbewegung-like behavior discussed in the recent literature. The early-time and long-time limits of the momentum expectation value and its time derivative demonstrate that the resistance to Bloch acceleration after initial band injection varies from real mass to effective mass dynamics as the electron accelerates through the band under the influence of electric field. This changing inertia from early injection of a free-mass electron is the result of the {\it real mass} electron {\it dressing-up} into the states of the crystal to become {\it an effective mass} electron. The ramifications of this temporal {\it dressing} behavior are discussed in considering the general dynamics of Bloch electrons subject to ultrastrong electric fields.
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