Random‐walk theory for localization

摘要: A continuous-time random-walk theory has been developed for Anderson localization. On a continuous time scale random walks are performed along extended (i.e., propagating) and localized trap) states. Complete information of disorder is contained in distribution function called “hopping function” ψnm(t), which gives the probability per unit transition from state m to n t. The “stay-put” (t = ∞), rediscover an excitation at site “0” t ∞ if it was there 0, obtained terms ψnm(t). Appropriate forms ψnm(t) constructed conformity with photoconductivity experiments on dispersive transport, (∞) calculated. results indicate that entire spectrum consists three regimes, namely, those (i) “diffusion,” (ii) “weak diffusion,” (iii) “no which, respectively, designate extension, power-law localization, exponential localization also shed light question “continuous or discontinuous (?)” across mobility edge.