A Vibrational Shortcut to the Mean First Passage Time


  Shlomi Reuveni [1,2]  ,  Rony Granek [3]  ,  Joseph Klafter [1]  
[1] School of Chemistry, Tel-Aviv University
[2] School of Mathematics, Tel-Aviv University
[3] Department of Biotechnology Engineering, Ben-Gurion University

What is the average time a random walker takes to get from A to B on a fractal structure and how does this mean time scale with the size of the system and the distance between source and target? We take a non-probabilistic approach towards this problem and show how the solution is readily obtained using an analysis of thermal vibrations on fractals. Our result emphasizes the duality between diffusion and vibrations on fractal structures, applications to biological systems are discussed.