Holographic Butterfly Effect and Diffusion in Quantum Critical Region

We investigate the butterfly effect and charge diffusion near the quantum phase transition in holographic approach. We argue that their criticality is controlled by the holographic scaling geometry with deformations induced by a relevant operator at finite temperature. Specifically, in the quantum critical region controlled by a single fixed point, the butterfly velocity decreases when deviating from the critical point. While, in the non-critical region, the behavior of the butterfly velocity depends on the specific phase at low temperature. Moreover, in the holographic Berezinskii-Kosterlitz-Thouless transition, the universal behavior of the butterfly velocity is absent. Finally, the tendency of our holographic results matches with the numerical results of Bose-Hubbard model. A comparison between our result and that in the $O(N)$ nonlinear sigma model is also given.Comment: 41 pages, 7 figures, minor revisions, refs adde

Holographic Shear Viscosity in Hyperscaling Violating Theories without Translational Invariance

In this paper we investigate the ratio of shear viscosity to entropy density, $\eta/s$, in hyperscaling violating geometry with lattice structure. We show that the scaling relation with hyperscaling violation gives a strong constraint to the mass of graviton and usually leads to a power law of temperature, $\eta/s\sim T^\kappa$. We find the exponent $\kappa$ can be greater than two such that the new bound for viscosity raised in arXiv:1601.02757 is violated. Our above observation is testified by constructing specific solutions with UV completion in various holographic models. Finally, we compare the boundedness of $\kappa$ with the behavior of entanglement entropy and conjecture a relation between them.Comment: 38 pages, 8 figures: 1 appendix added, 2 figures added, 1 references adde

TTˉT\bar T deformation on multi-quantum mechanics and regenesis

We study the $T\bar T$ deformation on a multi-quantum mechanical systems. By introducing the dynamical coordinate transformation, we obtain the deformed theory as well as the solution. We further study the thermo-field-double state under the $T\bar T$ deformation on these systems, including conformal quantum mechanical system, the Sachdev-Ye-Kitaev model, and the model satisfying Eigenstate Thermalization Hypothesis. We find common regenesis phenomena where the signal injected into one local system can regenerate from the other local system. From the bulk picture, we study the deformation on Jackiw-Teitelboim gravity governed by Schwarzian action and find that the regenesis phenomena here are not related to the causal structure of semi-classical wormhole.Comment: 20 pages, 5 figure

Wormholes and the Thermodynamic Arrow of Time

In classical thermodynamics, heat cannot spontaneously pass from a colder system to a hotter system, which is called the thermodynamic arrow of time. However, if the initial states are entangled, the direction of the thermodynamic arrow of time may not be guaranteed. Here we take the thermofield double state at $0+1$ dimension as the initial state and assume its gravity duality to be the eternal black hole in AdS$_2$ space. We make the temperature difference between the two sides by changing the Hamiltonian. We turn on proper interaction between the two sides and calculate the changes in energy and entropy. The energy transfer, as well as the thermodynamic arrow of time, are mainly determined by the competition between two channels: thermal diffusion and anomalous heat flow. The former is not related to the wormhole and obeys the thermodynamic arrow of time; the latter is related to the wormhole and reverses the thermodynamic arrow of time, i.e. transfer energy from the colder side to the hotter side at the cost of entanglement consumption. Finally, we find that the thermal diffusion wins the competition, and the whole thermodynamic arrow of time has not been reversed.Comment: 37 pages, 21 figures; v2: minor corrections and updated figure