Abstract:
    Since the concept of wave localization in random media was first proposed by P.W. Anderson more than 50 years ago, Anderson localization has become an important phenomenon in condensed matter physics. The phenomenon is ubiquitous in wave propagation in random environments including electrons in dirty metals, classical waves in random media and matter waves in random potentials. In the first part of this talk, a brief introduction of the Anderson localization will be given. In particular, some important concept and theory will be mentioned and discussed such as the weak localization (WL) effect, which is the most important wave interference effect that causes the localization of waves, and the self-consistent localization theory (SCLT).  In 2000, SCLT was generalized to random systems in open media and the concept of position-dependent diffusion coefficient was introduced. 
    In the second part of my talk, some results of our recent studies on the static and dynamic transport of localized waves in both one-dimensional and quasi-one-dimensional open media will be presented. In particular, it will be shown that the SCLT with position-dependent diffusion coefficient fails to describe the dynamical microwave transmission measurements at long times.  This strongly indicates the importance of resonant transmissions in the transport of waves in localized samples. A dynamic single parameter scaling model that incorporates only isolated resonant transmissions and ignores necklace states will be discussed. In the static limit, an analytic result obtained by using supersymmetric field theory will be presented. It is shown that the theory is capable of capturing all rare resonant transmissions and gives rise to a novel scaling behavior for the local diffusion coefficient.