Sinai Diffusion at Quasi-1D Topological Phase Transitions

We consider critical quantum transport in disordered topological quantum wires at the transition between phases with different topological indexes. Focusing on the example of thermal transport in class D (`Majorana') quantum wires, we identify a transport universality class distinguished for anomalous retardation in the propagation of excitations -- a quantum generalization of Sinai diffusion. We discuss the expected manifestations of this transport mechanism for heat propagation in topological superconductors near criticality and provide a microscopic theory explaining the phenomenon.