标题： 反作用对岛屿、Page曲线和互信息的影响 显示英文标题

标题： Effect of backreaction on Island, Page curve and Mutual Information

摘要： 我们计算了与变形的永恒AdS黑洞相连的浴体中霍金辐射的纠缠熵。 这个黑洞对应于两个相同且强耦合的大规模$N_c$热场理论，其中每个理论都因均匀静态分布的重基本夸克的存在而受到反作用（变形）。 在我们的观察中发现，霍金辐射的纠缠熵在早期时间以二次方式增加，在晚期时间以线性方式增加。 霍金辐射纠缠熵的大时间表达式用于找到Page曲线和 Page时间。 Page时间之后，由于岛屿的出现，纠缠熵趋于饱和到一个常数值。 我们观察到引入变形（反作用）会延迟岛屿的出现，并将Page曲线向更晚的时间移动。 随后，对快速混合时间的计算显示，随着反作用参数的增加而增加，这表明在存在变形的情况下信息检索需要更长的时间。 此外，我们对辐射子系统之间的互信息分析显示，在Page时间之前，它在临界时间消失，该时间随着变形的增加而增加。 Page时间之后，岛屿的出现导致黑洞子系统之间的互信息消失，并给出与快速混合时间同阶的时间差。 显示英文摘要

摘要： We compute the entanglement entropy of Hawking radiation in a bath attached to a deformed eternal AdS black hole. This black hole is dual to the two identical strongly coupled large-$N_c$ thermal field theories, where each theory is backreacted (deformed) by the presence of a uniform static distribution of heavy fundamental quarks. In our observation we find that the entanglement entropy of Hawking radiation increases in a quadratic manner for an early time and linearly for the late time. The large time expression for the entanglement entropy of Hawking radiation is used to find the Page curve and Page time. After the Page time, the entanglement entropy saturates to a constant value due to the appearance of an island. We observe that introducing deformation (backreaction) delays the appearance of island and shifts the Page curve to a later time. Subsequently, the computation of the scrambling time reveals an increase with the backreaction parameter, suggesting a longer duration for information retrieval in the presence of deformation. Moreover, our analysis of the mutual information between the radiation subsystems shows that it vanishes at a critical time which increases with the deformation before the Page time. After the Page time, the appearance of island leads to the vanishing of mutual information between black hole subsystems and gives the time difference of the order of scrambling time.