Report on scipost_202004_00049v1

Abstract

In classical probability theory, the term cutoff describes the property of some Markov chains to jump from (close to) their initial configuration to (close to) completely mixed in a very narrow window of time. We investigate how coherent quantum evolution affects the mixing properties in two fermionic quantum models (the "gain/loss" and "topological" models), whose time evolution is governed by a Lindblad equation quadratic in fermionic operators, allowing for a straightforward exact solution. We check that the cutoff phenomenon extends to the quantum case and examine how the mixing properties depend on the initial state. In the topological case, we further show how the mixing properties are affected by the presence of a long-lived edge zero mode when taking open boundary conditions. Contents 5.4 Effect of the edge mode 23 6 Conclusions 24 A Random walk on the hypercube 26 B Asymptotic expressions for the various distances 27 References 28