Correspondence of phase transition points and singularities of thermodynamic geometry of black holes

We explore a formulation of thermodynamic geometry of black holes and prove that the divergent points of the specific heat correspond exactly to the singularities of the thermodynamic curvature. We investigate this correspondence for different types of black holes. This formulation can also be applied to an arbitrary thermodynamic system.Comment: 10 pages, 4 figures, typos fixed, references adde

Non-Abelian Aharonov-Bohm effect with the time-dependent gauge fields

We investigate the non-Abelian Aharonov-Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of $SU(N)$ generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect.Comment: 4 page

Diffusivities bounds in the presence of Weyl corrections

In this paper, we investigate the behavior of the thermoelectric DC conductivities in the presence of Weyl corrections with momentum dissipation in the incoherent limit. Moreover, we compute the butterfly velocity and study the charge and energy diffusion with broken translational symmetry. Our results show that the Weyl coupling $\gamma$, violates the bounds on the charge and energy diffusivity. It is also shown that the Weyl corrections violate the bound on the DC electrical conductivity in the incoherent limit.Comment: v4: The appendix D and E were adde

Holographic Complexity in Gauge/String Superconductors

Following a methodology similar to \cite{Alishahiha:2015rta}, we derive a holographic complexity for two dimensional holographic superconductors (gauge/string superconductors) with backreactions. Applying a perturbation method proposed by Kanno in Ref. \cite{kanno}, we study behaviors of the complexity for a dual quantum system near critical points. We show that when a system moves from the normal phase ($T>T_c$) to the superconductor phase ($T<T_c$), the holographic complexity will be divergent.Comment: 6 page