Transport Properties Of 3 D Holographic Systems With Momentum Dissipation

The holographic principle offers a novel and effective tool for understanding the dynamics of quantum many-body systems with high coupling.A tangible embodiment of this idea is the AdS/CFT dual theory proposed from string theory.The AdS/CFT duality states that the associated dynamics of highly coupled systems on the boundary can be addressed using weakly coupled classical gravity theory,whereas the problem of gravitational quantization may be investigated using the holographic dictionary..In the realm of condensed matter physics,the AdS/CFT duality has been widely researched.Significant work has been achieved in the fields of holographic superconductivity,holographic Fermi systems,and holographic metal-insulation phase transitions,among others.Using holographic superconductivity as an example,the AdS/CFT duality addresses similar difficulties in high-temperature superconductivity,whereas Gubser and Hartnoll superconductivity 's model solves analogous problems in low-temperature superconductivity.The transport properties of the system are analytically explored,as well as the features of thermal conductivity and the coupling parameter pair under the system,in this study,which is based on the construction of an effective theory of 3D holography with gauge-axion coupling.Transport characteristics have an impact.In this paper,by constructing an effective theory of 3D holography with gauge-axion coupling,under the background of the newly constructed model,the transport properties of the system are analytically studied,and the characteristics of thermal conductivity and the coupling parameter pair under the system are studied.The effects of transport properties.The results show that the background solution of the 3D axion model is not related to the introduction of gauge-axion coupling.Through analytical analysis,it is found that the holographic DC conductivity of the three-dimensional linear axion model is temperature-dependent,which is different from the DC conductivity of the four-dimensional linear axion model,which is temperature-dependent.At the same time,it is found that the introduction of gauge-axion causes the model to undergo a metal-insulation phase transition at zero temperature.In addition,other DC thermal conductivity properties were analyzed and discussed,and finally we found that our model violated the Wiedemann-Franz(WF)law.In addition,through the analysis under the zero temperature limit and the strong momentum dissipation limit,it is found that according to the positive definiteness of the DC conductivity,the range of the gauge-axion coupling parameter is given:-1?J?1.In the appendix,we further examine the spectrum of the quasi-normal mode of the vector mode at zero charge density and find that when the gauge axion coupling is in the range of-1?J?1,the system at zero charge density is perturbed by the vector mode under the perturbation of the vector mode.is stable.Finally,we also check that the graviton mass of the vector mode under finite charge density is real within-1?J?1.Therefore,the vector mode is stable when the gauge axion coupling is in the range of-1?J?1.