Anderson localization of onedimensional hybrid particles
Abstract
We solve the Anderson localization problem on a twoleg ladder by the FokkerPlanck 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 DorokhovMelloPereyraKumar (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 disorderfree 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.
 Publication:

Physical Review B
 Pub Date:
 July 2012
 DOI:
 10.1103/PhysRevB.86.014205
 arXiv:
 arXiv:1205.3278
 Bibcode:
 2012PhRvB..86a4205X
 Keywords:

 72.15.Rn;
 71.36.+c;
 72.70.+m;
 73.23.b;
 Localization effects;
 Polaritons;
 Noise processes and phenomena;
 Electronic transport in mesoscopic systems;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 31 pages, 13 figures