Dynamical generation of Majorana edge correlations in a ramped Kitaev chain coupled to nonthermal dissipative channels

We quantitatively study the out-of-equilibrium edge-Majorana correlation in a linearly ramped one-dimensional Kitaev chain of finite length in a dissipative environment. The chemical potential is dynamically ramped to drive the chain from its topologically trivial to nontrivial phase in the presence of couplings to nonthermal Markovian baths. We consider two distinctive situations: In the first situation, the bath is quasilocal in the site basis (local in quasiparticle basis) while in the other it is local. Following a Lindbladian approach, we compute the early time dynamics as well as the asymptotic behavior of the edge-Majorana correlation to probe the interplay between two competing timescales - one due to the coherent ramping while the other to the dissipative coupling. For the quasilocal bath, we establish that there is a steady generation of Majorana correlations in asymptotic time and the presence of an optimal ramping time which facilitates a quicker approach to the topological steady state. In the second scenario, we analyze the action of a local particle-loss type of bath in which we have established the existence of an optimal ramping time which results from the competing dynamics between the unitary ramp and the dissipative coupling. While the defect generated by the former decays exponentially with increasing ramp duration, the later scales linearly with the same. This linear scaling is further established through a perturbation theory formulated using the nondimensionalized coupling to the bath as a small parameter.