量子场论中的量子疤痕
Quantum Scars in Quantum Field Theory
AI总结：
本文发展了量子场论中的量子疤痕理论，推广Heller和Bogomolny形式，发现不稳定周期经典解在能量本征函数上留下印记，破坏特定能量尺度的热化，并以Q-cloud为例验证，同时探讨与里德伯原子阵列多体疤痕的联系。
摘要：
我们发展了量子场的量子疤痕理论。通过将Heller和Bogomolny的形式从少体量子力学推广到量子场，我们发现场方程的不稳定周期经典解以精确的方式印记在能量本征函数的能带上。这表明在特定能量尺度上热化被破坏，其方式可通过半经典理论表征。作为明确示例，我们考虑了复标量场理论中的时间周期非拓扑孤子。我们发现一种不稳定的Q-ball变体，称为Q-cloud，会诱发量子疤痕。我们工作的若干技术贡献包括表征场论中周期轨道模空间的方法，这些方法对于构建我们的量子疤痕公式至关重要。我们进一步讨论了与里德伯原子阵列中量子多体疤痕的潜在联系。
英文摘要：
We develop the theory of quantum scars for quantum fields. By generalizing the formalisms of Heller and Bogomolny from few-body quantum mechanics to quantum fields, we find that unstable periodic classical solutions of the field equations imprint themselves in a precise manner on bands of energy eigenfunctions. This indicates a breakdown of thermalization at certain energy scales, in a manner that can be characterized via semiclassics. As an explicit example, we consider time-periodic non-topological solitons in complex scalar field theories. We find that an unstable variant of Q-balls, called Q-clouds, induce quantum scars. Some technical contributions of our work include methods for characterizing moduli spaces of periodic orbits in field theories, which are essential for formulating our quantum scar formula. We further discuss potential connections with quantum many-body scars in Rydberg atom arrays.
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