2011/01/31 by P L Krapivsky, P. L. Krapivsky, J M Luck +1
Mathematics · Physics and Astronomy · #Bipartite graph #Chain (unit) #Dynamics (music) #Moment (physics) #Particle (ecology) #Position (finance) #Quantum #Quantum and electron transport phenomena #Quantum dynamics #Quantum many-body systems #Quantum particle #Spectral Theory in Mathematical Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2011/02/p02031
published as J. Stat. Mech. (2011) P02031 · 20 pages, 12 figures, 1 table. Note added on the recent work by Lepri et al
arxiv created 2011/02/18 · openalex publication_date 2011/02/18 · arxiv updated 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some special energies. We provide a consistent picture for two well-known one-dimensional examples: the chain with off-diagonal disorder and the random-dimer model. In both cases the quantum motion exhibits a peculiar kind of anomalous diffusion which can be referred to as bi-fractality. The disorder-averaged density profile of the particle becomes critical in the long-time regime. The q th moment of the position of the particle diverges with time whenever q exceeds some q 0 . We obtain q 0 = 2 for off-diagonal disorder on the chain (and conjecturally on two-dimensional bipartite lattices as well). For the random-dimer model, our result q 0 = 1/2 corroborates known rigorous results.