论文标题
量子多体系统和重力中平衡的纯状态的纠缠熵
Entanglement entropies of equilibrated pure states in quantum many-body systems and gravity
论文作者
论文摘要
我们在不可融合的多体系统中为纯状态的纯状状态的肾脏熵开发了通用近似，宏观上类似于平衡密度矩阵。所得的表达式由相关平衡密度矩阵的性质完全确定，因此与初始状态的细节无关，同时也与单一的时间进化显然一致。对于重力系统中的平衡纯状态，例如涉及黑洞的纯状态，这种近似为使用欧几里得路径积分来计算纠缠熵的处方，这与统一性一致，因此可以用来解决霍金的信息损失悖论。它应用于最近蒸发黑洞和永恒的黑洞与浴缸的模型，它提供了复制虫洞的推导，并阐明了它们的数学和物理起源。特别是，它表明复制虫洞可能在具有固定的哈密顿量的系统中出现，而无需合奏平均。
We develop a universal approximation for the Renyi entropies of a pure state at late times in a non-integrable many-body system, which macroscopically resembles an equilibrium density matrix. The resulting expressions are fully determined by properties of the associated equilibrium density matrix, and are hence independent of the details of the initial state, while also being manifestly consistent with unitary time-evolution. For equilibrated pure states in gravity systems, such as those involving black holes, this approximation gives a prescription for calculating entanglement entropies using Euclidean path integrals which is consistent with unitarity and hence can be used to address the information loss paradox of Hawking. Applied to recent models of evaporating black holes and eternal black holes coupled to baths, it provides a derivation of replica wormholes, and elucidates their mathematical and physical origins. In particular, it shows that replica wormholes can arise in a system with a fixed Hamiltonian, without the need for ensemble averages.
