On The Universality Of Diffusion Bounds In Holographic Systems

The transport properties of strongly coupled systems have long been a topic of importance in condensed physics as well as high energy physics.As a powerful tool of studying strongly coupled systems,the holographic duality reveals some universal behaviors of the transport phenomena that do not relay on the microscopic details but are determined by the symmetries of the system.Previous studies show that some diffusive processes dominated by hydrodynamic modes are restricted by the quantum chaotic properties of the strongly coupled systems and causality.As a result,the related diffusivities are bounded as well.It has been clear that the lower bound of the diffusivities is determined by the butterfly velocity and the Lyapunov exponent of the system.Nevertheless,the identification of a characteristic velocity and a timescale bounding above the diffusivities is still an open question.Recently,it has been shown that,one can define the convergence of the hydrodynamics through the collision between hydrodynamic modes and non-hydrodynamic modes in the complex plane of the frequency.Note that this is not only a requirement of the causality but also promises a systematical way to identify a characteristic velocity and a timescale to bound the diffusivities.In this thesis,we firstly take a brief review on the previous studies of diffusion bounds in holographic models.Then,we shortly introduce the basic ideas of the holographic duality.After that,we focus on analyzing a wide class of strongly coupled systems with breakings of translational symmetry through the holographic axion model and numeric methods.Our results show that the diffusive modes are indeed bounded from above by the convergence of the hydrodynamics.Moreover,the upper bound meets exactly the lower bound set by quantum chaos,hence resulting in a unique value of diffusivities in the infrared(also low temperature)limit.