截断的马约拉纳费米子
A Truncated Majorana
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中文总结 AI 辅助
该研究通过随时间变化的通道快门截断马约拉纳波包，分析其量子场动力学，揭示了全局红外记忆与局域因果截断的互补性，为拓扑平台的时变控制提供场论基础。
中文摘要 AI 辅助
我们研究了通过随时间变化的通道快门截断马约拉纳波包的量子场动力学。将截断建模为手性传播的受控修改而非字面意义上的空间切割，我们分析了1+1维无质量马约拉纳场在其手性分量间随时间变化的旋转作用下的情况。我们证明该方案呈现出两个互补的物理极限：全局上，早期与晚期通道识别的不匹配会诱导费米子Bogoliubov变换，我们证明这种渐近变化会普遍产生红外软模记忆β(ω,ν)∝(ω+ν)⁻¹，导致希尔伯特-施密特范数出现对数发散，这种类似正交灾难的阻碍即使在无质量极限下无限平滑切换时仍然存在；相反，在对产生消失的粒子数守恒区域，快门充当纯因果滤波器，我们建立了精确的局域场恒等式，表明在偶局域可观测量代数的限制下，保留的部分恰好等价于单粒子态，而丢弃的部分则退化为真空。最终，我们证明全局红外记忆与局域因果截断是同一动力学操作的互补诊断，这些结果为拓扑平台中的随时间变化控制提供了严格的场论基础，将有效操作基准与微观边界动力学清晰区分开来。
英文摘要
A Majorana field cannot be split into two spatial pieces, but a propagating Majorana can be truncated by a time-dependent shutter. We study this truncation for the two chiral components of a massless Majorana field in one spatial dimension, modeling the shutter as a smooth time-dependent $SO(2)$ rotation of the two components. Although orthogonal at the level of the real field algebra, this rotation does not preserve the positive- and negative-frequency splitting that defines the Fock vacuum, so the in-vacuum becomes a fermionic squeezed state in outgoing modes. At any finite infrared regulator, a single incident Majorana is then a single outgoing quasiparticle on top of this squeezed vacuum. The squeezed background carries a universal soft response: its anomalous Bogoliubov kernel falls as the inverse sum of the two frequencies at low energy, so the anomalous Hilbert--Schmidt norm grows logarithmically with the infrared cutoff, with a coefficient fixed by the asymptotic shutter mismatch. The vacuum overlap exhibits a Fermi-edge type orthogonality exponent which, for the rotation-angle lift $Δθ$ with $|Δθ|<π$, is exactly $(Δθ/2π)^2$, in analogy with the Fermi-edge singularity and the Kondo and Luttinger-liquid problems. We prove local equivalence non-perturbatively for the squeezed-vacuum factor under a compact-support hypothesis, and give an exact local pullback identity for the full one-quasiparticle state on the even CAR algebra; combined with wavepacket-localization assumptions, these yield the expected local vacuum and one-Majorana descriptions. We verify profile independence using a smooth switching family and contrast the temporal benchmark with a number-conserving beam-splitter benchmark whose entropy is bounded by $\log 2$.
发表机构
- Kharazmi University（卡拉兹米大学）
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