Mixing times and cutoffs in open quadratic fermionic systems

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 phenomenon of cutoff extends to the quantum case and examine with some care how the mixing properties depend on the initial state, drawing different regimes of our models with qualitatively different behaviour. 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.