标题： 低能有效理论：非整数电荷电子波包的局域化-去局域化转变 显示英文标题

标题： Low-energy effective theory of localization-delocalization transition in noninteger-charged electron wave packets

摘要： 我们提出了一种低能有效理论来描述波函数的定域-去定域转变，这种转变发生在通过带有非整数磁通量子的电压脉冲单独注入电子和空穴时。 我们发现，这种转变可以用截断的低能空间中的有效散射矩阵来描述，该矩阵由两部分组成。 第一部分描述了散射矩阵的红外发散，而第二部分代表高能关联。 对于衰减比洛伦兹型更快的短尾脉冲，散射矩阵在红外极限下仅表现出逆线性发散。 这种发散导致动力学正交灾难，从而产生具有去定域波函数的电子-空穴对。 相比之下，高能关联可以通过一个常数项来近似，这会导致具有定域波函数的电子-空穴对。 由于这两部分之间的竞争，波函数可能会经历定域-去定域转变，这种转变发生在通过电压脉冲单独注入的电子和空穴中。 因此，所有短尾脉冲的定域-去定域转变都可以用相同的有效散射矩阵来描述，这表明它们属于同一个普适类。 对于具有更长尾部的脉冲，散射矩阵可能表现出额外的红外发散。 我们证明了洛伦兹型脉冲会产生对数发散，而分数幂洛伦兹型脉冲会产生幂律发散。 这些额外的发散可能导致属于不同普适类的定域-去定域转变。 这些结果展示了时间依赖量子输运中定域-去定域转变的精细调节能力。 显示英文摘要

摘要： We present a low-energy effective theory to describe the localization-delocalization transition, which occurs for wave functions of electrons and holes injected individually by a voltage pulse with noninteger flux quantum. We find that the transition can be described by an effective scattering matrix in a truncated low-energy space, which is composed of two parts. The first part describes the infrared-divergence of the scattering matrix, while the second part represents the high-energy correlation. For short-tailed pulses which decay faster than Lorentzian, the scattering matrix exhibits solely an inverse linear divergence in the infrared limit. The divergence is responsible for the dynamical orthogonality catastrophe, which leads to electron-hole pairs with delocalized wave functions. In contrast, the high-energy correlation can be approximated by a constant term, which leads to electron-hole pairs with localized wave functions. Due to the competition between the two terms, the wave functions can undergo a localization-delocalization transition, which occurs for electrons and holes injected individually by the voltage pulse. As a consequence, the localization-delocalization transitions for all short-tailed pulses can be described by the same effective scattering matrix, suggesting that they belong to the same universality class. For pulses with longer tails, the scattering matrix can exhibit additional infrared-divergences. We show that a Lorentzian pulse gives rise to a logarithmic divergence, while a fractional-powered Lorentzian pulse gives rise to a power-law divergence. The additional divergence can lead to localization-delocalization transitions belonging to different universality classes. These results demonstrate the fine-tuning capabilities of the localization-delocalization transition in time-dependent quantum transport.