SYK可解模型中强相互作用费米子超流体的衰减动力学
Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models
AI总结：
本文通过构造类SYK模型并结合大N近似与格林函数方法，研究一维BCS系统中强相互作用对费米子超流体淬火动力学的影响，发现强SYK相互作用抑制配对序并导致系统快速热化，使振荡强度迅速衰减，且衰减率遵循可由玻尔兹曼方程解释的标度律。
摘要：
费米子超流体的淬火动力学在实验和理论两方面都是一个活跃的课题。利用BCS理论，这类非平衡问题可以约化为近独立的自旋动力学，仅含有一个时间相关的平均场配对项。这导致在某些参数区域内配对强度出现持续振荡。然而，实验观察到当相互作用变强时，例如在幺正费米气体中，振荡会迅速衰减。关于这一问题的理论分析目前仍然缺乏。在本工作中，我们构造了一个类SYK模型，用以分析一维BCS系统中强相互作用的影响。我们采用大N近似和基于格林函数的技术来求解平衡问题和淬火动力学。我们的研究结果表明，强SYK相互作用会抑制配对序。此外，我们验证了在存在SYK相互作用时系统会迅速热化，无论其涉及内禀配对序还是邻近效应，都会导致振荡强度的快速衰减。衰减率对SYK相互作用表现出不同的标度律，这可以通过玻尔兹曼方程来理解。本工作代表了理解强相互作用费米子超流体衰减动力学的第一步。
英文摘要：
Quench dynamics of fermionic superfluids are an active topic both experimentally and theoretically. Using the BCS theory, such non-equilibrium problems can be reduced to nearly independent spin dynamics, only with a time-dependent mean-field pairing term. This results in persisting oscillations of the pairing strength in certain parameter regimes. However, experiments have observed that the oscillations decay rapidly when the interaction becomes strong, such as in the unitary Fermi gas. Theoretical analysis on this matter is still absent. In this work, we construct an SYK-like model to analyze the effect of strong interactions in a one-dimensional BCS system. We employ the large-$N$ approximation and a Green's function-based technique to solve the equilibrium problem and quench dynamics. Our findings reveal that a strong SYK interaction suppresses the pairing order. Additionally, we verify that the system quickly thermalizes with SYK interactions, whether it involves intrinsic pairing order or proximity effect, resulting in a rapid decay of the oscillation strength. The decay rates exhibit different scaling laws against SYK interaction, which can be understood in terms of the Boltzmann equation. This work represents a first step towards understanding the attenuating dynamics of strongly interacting fermionic superfluids.
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