Holographic evolution of the mutual information

Hubeny, Veronika E., Rangamani, Mukund

Dmitry Sergeevich Ageev, I. Ya. Aref’eva

Using holographic methods, we study the heating up process in quantum field theory. As a holographic dual of this process, we use absorption of a thin shell on a black brane. We find the explicit form of the time evolution of the quantum mutual information during heating up from the temperature Ti to the temperature T f in a system of two intervals in two-dimensional space–time. We determine the geometric characteristics of the system under which the time dependence of the mutual information has a bell shape: it is equal to zero at the initial instant, becomes positive at some subsequent instant, further attains its maximum, and again decreases to zero. Such a behavior of the mutual information occurs in the process of photosynthesis. We show that if the distance x between the intervals is less than log 2/2π T i , then the evolution of the holographic mutual information has a bell shape only for intervals whose lengths are bounded from above and below. For sufficiently large x , i.e., for x < log 2/2π T i , the bell-like shape of the time dependence of the quantum mutual information is present only for sufficiently large intervals. Moreover, the zone narrows as T i increases and widens as T f increases.

David D. Blanco, Horacio Casini, Ling-Yan Hung +1 more

I. Ya. Aref’ eva, Igor Vasil'evich Volovich, Oleg Valerievich Inozemcev

We analyze how the compositeness of a system affects the characteristic time of equilibration. We study the dynamics of open composite quantum systems strongly coupled to the environment after a quantum perturbation accompanied by nonequilibrium heating. We use a holographic description of the evolution of entanglement entropy. The nonsmooth character of the evolution with holographic entanglement is a general feature of composite systems, which demonstrate a dynamical change of topology in the bulk space and a jumplike velocity change of entanglement entropy propagation. Moreover, the number of jumps depends on the system configuration and especially on the number of composite parts. The evolution of the mutual information of two composite systems inherits these jumps. We present a detailed study of the mutual information for two subsystems with one of them being bipartite. We find five qualitatively different types of behavior of the mutual information dynamics and indicate the corresponding regions of the system parameters.

Mohsen Alishahiha, M. Reza Mohammadi Mozaffar, Mohammad Reza Tanhayi

Peng Liu, Chao Niu, Jian-Pin Wu

We study the effect of anisotropy on holographic entanglement entropy (HEE) and holographic mutual information (MI) in the Q-lattice model, by exploring the HEE and MI for infinite strips along arbitrary directions. We find that the lattice always enhances the HEE. The MI, however, is enhanced by lattice for large sub-regions; while for small sub-regions, the MI is suppressed by the lattice. We also discuss how these phenomena result from the deformation of geometry caused by Q-lattices.