Wannier-Stark ladder in the linear absorption of a random system with scale-free disorder

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We study numerically the linear optical response of a quasiparticle moving on a one-dimensional disordered lattice in the presence of a linear bias. The random site potential is assumed to be long-range-correlated with a power-law spectral density S(k) 1/kα, α> 0. This type of correlations results in a phase of extended states at the band center, provided α is larger than a critical value αc [F. A. B. F. de Moura and M. L. Lyra, Phys. Rev. Lett. 81, 3735 (1998)]. The width of the delocalized phase can be tested by applying an external electric field: Bloch-like oscillations of a quasiparticle wave packet are governed by the two mobility edges, playing now the role of band edges [F. Domınguez-Adame et al., Phys. Rev. Lett. 91, 197402 (2003)]. We demonstrate that the frequency-domain counterpart of these oscillations, the so-called Wannier-Stark ladder, also arises in this system. When the phase of extended states emerges in the system, this ladder turns out to be a comb of doublets, for some range of disorder strength and bias. Linear optical absorption provides a tool to detect this level structure.