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We show that Anderson localization in quasi-one dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron trajectories only. At large length scales, an exponential proliferation of trajectories of nearly identical classical action generates an abundance of interference terms, which eventually leads to a suppression of transport coefficients. We quantitatively describe this mechanism in two different ways: the explicit description of transition probabilities in terms of interfering trajectories, and an hierarchical integration over fluctuations in the classical phase space of the array cavities.
We present a trajectory-based semiclassical calculation of the full counting statistics of quantum transport through chaotic cavities, in the regime of many open channels. Our method to obtain the $m$th moment of the density of transmission eigenvalu
We consider the dynamics of an electron in an infinite disordered metallic wire. We derive exact expressions for the probability of diffusive return to the starting point in a given time. The result is valid for wires with or without time-reversal sy
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. W
We construct a model to study the localization properties of nanowires of dopants in silicon (Si) fabricated by precise ionic implantation or STM lithography. Experiments have shown that Ohms law holds in some cases, in apparent defiance to the Ander
Optomechanical arrays are a promising future platform for studies of transport, many-body dynamics, quantum control and topological effects in systems of coupled photon and phonon modes. We introduce disordered optomechanical arrays, focusing on feat