2012/05/31 by Hong-Yi Xie, Vladimir E. Kravtsov, V. E. Kravtsov +1 · 2 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics #Random lasers and scattering media #Statistical physics #Strong Light-Matter Interactions #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.86.014205
published as Phys. Rev. B 86, 014205 (2012) · 31 pages, 13 figures
arxiv created 2012/07/18 · openalex publication_date 2012/07/18 · arxiv updated 2012/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We solve the Anderson localization problem on a two-leg ladder by the Fokker-Planck equation approach. The solution is exact in the weak disorder limit at a fixed interchain coupling. The study is motivated by progress in investigating the hybrid particles such as cavity polaritons. This application corresponds to parametrically different intrachain hopping integrals (a ``fast'' chain coupled to a ``slow'' chain). We show that the canonical Dorokhov-Mello-Pereyra-Kumar (DMPK) equation is insufficient for this problem. Indeed, the angular variables describing the eigenvectors of the transmission matrix enter into an extended DMPK equation in a nontrivial way, being entangled with the two transmission eigenvalues. This extended DMPK equation is solved analytically and the two Lyapunov exponents are obtained as functions of the parameters of the disordered ladder. The main result of the paper is that near the resonance energy, where the dispersion curves of the two decoupled and disorder-free chains intersect, the localization properties of the ladder are dominated by those of the slow chain. Away from the resonance they are dominated by the fast chain: a local excitation on the slow chain may travel a distance of the order of the localization length of the fast chain.