Although stemming from different fields, not only the Continuous Time Random Walks and the Continuous Time Quantum Walks, but also extensions of the Rouse model, the fundamental model of polymer dynamics, have many features in common. This is due to the structure of the discrete Laplace operators present, which are needed to model temporal changes in systems described by graphs. I will thus recall situations appearing in classical transport [1], make the connection to the quantum situation [2] and give a short introduction to polymer dynamics [3]. In continuation, I will exemplify the common points and the differences between the models, also using very recent results [4].

[1] I.M. Sokolov, A.B. and J. Klafter, Fractional Kinetics, Physics Today, 55, 48, Nov. 2002.
[2] O. Mülken and A.B., Continuous Time Quantum Walks: Models for Coherent Transport on Complex Networks, Phys. Reports, 502, 37 (2011)
[3] A.A. Gurtovenko and A.B., Generalized Gaussian Structures: Models for Polymer Structures with Complex Topology, Adv. Polymer Sci., 182, 171 (2005)
[4] Z. Darázs, A. Anishchenko, T. Kiss, A.B. and O. Mülken, Transport Properties of Continuous Time Quantum Walks on Sierpinski Fractals, Phys. Rev. E 90, 032113 (2014)