A relation between massive scalar field in AdSd+1 and diffusion in channels

8th International Symposium on Quantum Theory and Symmetries

Romero, Juan M.^1 ; Gaona, Alejandro^1

Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, México, D.F 01120, Mexico^1

关键词: Conformal symmetry;    Dinger equation;    In-channels;    Jacobs equation;    Scalar fields;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/512/1/012028/pdf
DOI  :  10.1088/1742-6596/512/1/012028

来源: IOP

【 摘 要 】

It is shown that, when the diffusion coefficient is a constant and is taken a particular family of channels, the Fick-Jacobs equation is invariant under conformal symmetry. In addition, using the diffusion coefficient and the geometric parameters of the channels, a representation for the conformal algebra is obtained. Furthermore, it is found that for these systems the Fick-Jacobs equation is equivalent to the Schrodinger equation for the 1-dimensional conformal quantum mechanics. Moreover, using this equivalence, it is found a relation between a massive scalar field equation in AdSd+ibackground and Fick-Jacobs equation, where the geometric parameter of the channels and the geometric parameters of AdSd+1are identified.