论文标题
部分可观测时空混沌系统的无模型预测
Excited state quantum phase transition and Loschmidt echo spectra in a spinor Bose-Einstein condensate
论文作者
论文摘要
在实验可实现的量子多体系统中识别激发状态量子相变（ESQPTS）的动力学特征有助于理解ESQPT的动态效应。在这样的系统中，高度可控的旋转纺纱物玻璃体凝结物（BEC）为研究ESQPTS提供了卓越的平台。在这项工作中，我们通过Loschmidt Echo Spectrum研究了ESQPT以旋转$ 1 $ BEC的动态特性。 Loschmidt Echo频谱是众所周知的Loschmidt Echo的延伸，并确定为演变状态与初始汉密尔顿的激发状态之间的重叠。我们表明，随着系统穿过ESQPT的临界点，时间演变的时间和长期平均的Loschmidt Echo Spectrum都会发生显着变化。此外，Loschmidt回声频谱在临界点显示的特定行为是用于探测ESQPT的动力检测器。我们进一步演示了如何通过使用与Loschmidt Echo频谱相关的能量分布来捕获ESQPT的特征，以尊重时间和长时间的平均情况。我们的发现有助于进一步验证Loschmidt Echo Spectrum在见证多体系统中各种量子相变的实用性，并提供了一种新的方法来实验研究ESQPTS的动态后果。
Identifying dynamical signatures of excited state quantum phase transitions (ESQPTs) in experimentally realizable quantum many-body systems is helpful for understanding the dynamical effects of ESQPTs. In such systems, the highly controllable spinor Bose-Einstein condensates (BECs) offer an exceptional platform to study ESQPTs. In this work, we investigate the dynamical characteristics of the ESQPT in spin-$1$ BEC by means of the Loschmidt echo spectrum. The Loschmidt echo spectrum is an extension of the well-known Loschmidt echo and definded as the overlaps between the evolved state and the excited states of the initial Hamiltonian. We show that both the time evolved and long time averaged Loschmidt echo spectrum undergo a remarkable change as the system passes through the critical point of the ESQPT. Moreover, the particular behavior exhibited by the Loschmidt echo spectrum at the critical point stand as a dynamical detector for probing the ESQPT. We further demonstrate how to capture the features of the ESQPT by using the energy distribution associated with the Loschmidt echo spectrum for time evolved and long time averaged cases, respectrively. Our findings contribute to a further verification of the usefulness of the Loschmidt echo spectrum for witnessing various quantum phase transitions in many-body systems and provide a new way to experimentally examine the dynamical consequences of ESQPTs.
