Optimal dephasing for ballistic energy transfer in disordered linear chains

We study the interplay between dephasing, disorder, and coupling to a sink on transport efficiency in a one-dimensional chain of finite length N, and in particular the beneficial or detrimental effect of dephasing on transport. The excitation moves along the chain by coherent nearest-neighbor hopping Ω, under the action of static disorder W and dephasing γ. The last site is coupled to an external acceptor system (sink), where the excitation can be trapped with a rate Γtrap. While it is known that dephasing can help transport in the localized regime, here we show that dephasing can enhance energy transfer even in the ballistic regime. Specifically, in the localized regime we recover previous results, where the optimal dephasing is independent of the chain length and proportional to W or W2/Ω. In the ballistic regime, the optimal dephasing decreases as 1/N or 1/N, respectively, for weak and moderate static disorder. When focusing on the excitation starting at the beginning of the chain, dephasing can help excitation transfer only above a critical value of disorder Wcr, which strongly depends on the sink coupling strength Γtrap. Analytic solutions are obtained for short chains.