Anderson localization is a key mechanism for the emergence of non-ergodicity in disordered quantum systems. In this seminar, I will present some recent results which suggest that Anderson localization has glassy properties. This is addressed by following an analogy between Anderson localization and the physics of directed polymers, one of the simplest model of statistical physics in which disorder plays a non-trivial role, as in spin glasses. I will first describe the case of random graphs of effective infinite dimensionality which has attracted a strong interest recently due to its analogy with the problem of many body localization. Then, I will show the glassy properties of quantum transport in dimension two.
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