Calogero模型中的回波与缺陷
Echoes and defects in the Calogero model
AI总结：
本文研究时间调制谐振子势阱中Calogero模型的标度对称性与统计相互作用，揭示相互作用和排斥统计在基态回波振幅与保真度中的普适特征，发现增强相互作用促进缺陷增殖并抑制中间回波。
摘要：
在这项工作中，我们将标度对称性与统计之间的相互作用研究扩展到一维流体，具体研究了在时间调制的谐振子势阱中的Calogero模型。该模型可以解释为具有排斥统计的自由粒子，并且是一维中标度不变流体的一个例子，展现出谐振子势阱所保持的$\u005cmathrm{SO(2,1)}$动力学对称性。利用这一动力学对称性，我们研究了两种实验相关的驱动方案，涵盖准静态和非绝热区域，并在基态回波振幅和密切相关的基态保真度中揭示了相互作用和排斥统计的普适特征。特别地，在周期性调制和通过势阱频率无能隙点的缓慢驱动下，增强的相互作用和排斥被证明有利于缺陷的增殖并阻碍其湮灭，从而导致基态保真度和回波振幅的普适性下降。我们还表明，增加排斥会急剧抑制中间回波出现的可能性，这种抑制超出了周期性驱动与势阱固有频率的可公度性所规定的回波。
英文摘要：
In this work, we extend the study of the interplay between scaling symmetries and statistics to one-dimensional fluids by studying the Calogero model in a harmonic trap modulated through time. The latter harbors an interpretation in terms of free particles imbued with exclusion statistics and is an example of a scale invariant fluid in one-dimension displaying $\mathrm{SO(2,1)}$ dynamical symmetry preserved by harmonic traps. Taking advantage of the dynamical symmetry, two experimentally relevant drive protocols spanning both quasistatic and nonadiabatic regimes are investigated and universal signatures of the interactions and exclusion statistics are uncovered in the ground-state echo amplitude and closely related ground-state fidelity. In particular, under both periodic modulation and slow drive through the gapless point of the trap frequency, enhanced interactions and exclusion are shown to favor the proliferation of defects and to hinder their annihilation, which leads to a universal decrease of ground-state fidelities and echo amplitudes. We also show that increasing exclusion sparks a sharp suppression of the likelihood of intermediate echoes beyond those imposed by the commensurability of a periodic drive and the natural frequency of the trap.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
