标题： $ν$-QSSEP：随机扩散量子系统中纠缠传播的玩具模型 显示英文标题

标题： $ν$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems

摘要： 我们研究了所谓$QSSEP$模型的推广中的非平衡纠缠动力学，这是一个具有空间和时间随机跃迁幅度的自由费米子链。 在我们的设置中，噪声幅度是空间调制的，满足$\nu$位平移不变性，但在时间上保留其随机性。 对于每个噪声实现，动力学保持高斯性，这使得可以获得噪声平均的与纠缠相关的量。 稳态关联函数的统计满足具有拓扑性质的非平凡关系。 它们反映了在乘以结构化的动量依赖随机$SU(\nu)$矩阵下的 Haar 不变性。 我们详细讨论了$\nu=1$和$\nu=2$的情况。 对于$\nu=1$，即空间均匀噪声，我们表明纠缠动力学可以用准粒子图景的随机推广来描述。 确切地说，纠缠是由准粒子对传播的。 这些准粒子对的纠缠内容与确定性链相同。 然而，准粒子的轨迹是随机游走，导致扩散的纠缠增长。 显示英文摘要

摘要： We investigate out-of-equilibrium entanglement dynamics in a generalization of the so-called $QSSEP$ model, which is a free-fermion chain with stochastic in space and time hopping amplitudes. In our setup, the noisy amplitudes are spatially-modulated satisfying a $\nu$-site translation invariance but retaining their randomness in time. For each noise realization, the dynamics preserves Gaussianity, which allows to obtain noise-averaged entanglement-related quantities. The statistics of the steady-state correlators satisfy nontrivial relationships that are of topological nature. They reflect the Haar invariance under multiplication with structured momentum-dependent random $SU(\nu)$ matrices. We discuss in detail the case with $\nu=1$ and $\nu=2$. For $\nu=1$, i.e., spatially homogeneous noise we show that the entanglement dynamics is describable by a stochastic generalization of the quasiparticle picture. Precisely, entanglement is propagated by pairs of quasiparticles. The entanglement content of the pairs is the same as for the deterministic chain. However, the trajectories of the quasiparticles are random walks, giving rise to diffusive entanglement growth.