AI 中文总结
本文研究与损耗腔耦合的Yukawa-Sachdev-Ye-Kitaev模型，发现耗散可增强其 scrambling 效应，确定了临界玻色子费米子比γ_c≈2/p²，揭示了不同参数下的丰富动力学行为。
AI 中文摘要
我们研究Yukawa-Sachdev-Ye-Kitaev模型，这是一个由N个Majorana费米子和R=γN个玻色子组成的无序模型，其中玻色子与SYK p体相互作用的独立实现形式线性耦合，且处于由Lindblad主方程建模的耗散环境中。受量子模拟器中实现SYK模型的最新方案启发，我们聚焦于速率为κ的玻色子泄漏过程。将系统初始化至稳态后，我们分析了后期费米子弛豫速率与Lyapunov指数，通过数值求解大N理论及p很大时的极限情况，发现了丰富的动力学行为。最值得注意的是，对于任意κ值，Lyapunov指数均保持为正；当p>2时，Lyapunov指数甚至会随κ增大而增长。QED情形（p=2）介于完全混沌区域（p>2）与可积情形（p=1）之间，呈现出特殊性质。我们还确定了玻色子与费米子的临界比值γ_c≈2/p²，该比值可区分不同的动力学区域。
英文摘要
We study the Yukawa-Sachdev-Ye-Kitaev model, a disordered model of $N$ Majorana fermions and $R=γN$ bosons in which the bosons are linearly coupled to independent realizations of SYK $p$-body interactions, in the presence of dissipation, modeled by a Lindblad master equation. Motivated by recent proposals for implementing SYK models in quantum simulators, we focus on bosonic leakage at rate $κ$. Initializing the system in the steady state, we analyze the late-time fermionic relaxation rate and the Lyapunov exponent, solving the large-$N$ theory both numerically and for $p$ large, finding a rich landscape of dynamical behaviors. Most notably, the Lyapunov exponent remains positive for every value of $κ$ and, for $p>2$, can even grow as $κ$ increases. The QED case $p=2$, which lies between the fully chaotic regime $p>2$ and the integrable case $p=1$, exhibits special features. We also identify a critical value of the boson-to-fermion ratio $γ_c \approx 2/p^2$ separating distinct dynamical regimes.
Comments15 pages, 3 figures. v2: updated numerical results with better convergence, no substantial changes. Added data availability and repository for numerical codes
