2008/05/31 by Sergej Flach, S. Flach, Dmitry O. Krimer +2 · 326 citations
Computer Science · Physics and Astronomy · #Advanced Fiber Laser Technologies #Computer science #Condensed matter physics #Eigenvalues and eigenvectors #Moment (physics) #Network packet #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear system #Physics #Quantum mechanics #Second moment of area #Statistical physics #Transient (computer programming) #Wave packet #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.102.024101
published in Physical Review Letters 102(2), 024101 (American Physical Society) · 4 pages, 3 figures
openalex publication_date 2009/01/14 · arxiv created 2009/04/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the absence of nonlinearity all eigenmodes of a chain with disorder are spatially localized (Anderson localization). The width of the eigenvalue spectrum and the average eigenvalue spacing inside the localization volume set two frequency scales. An initially localized wave packet spreads in the presence of nonlinearity. Nonlinearity introduces frequency shifts, which define three different evolution outcomes: (i) localization as a transient, with subsequent subdiffusion; (ii) the absence of the transient and immediate subdiffusion; (iii) self-trapping of a part of the packet and subdiffusion of the remainder. The subdiffusive spreading is due to a finite number of packet modes being resonant. This number does not change on average and depends only on the disorder strength. Spreading is due to corresponding weak chaos inside the packet, which slowly heats the cold exterior. The second moment of the packet grows as t;alpha. We find alpha=1/3.