We consider a finite, disordered 1D quantum lattice with a side-attached impurity. We study theoretically the transport of a single electron from the impurity into the lattice, at zero temperature. The transport is dominated by Anderson localization and, in general, the electron motion has a random character due to the lattice disorder. However, we show that by adjusting the impurity energy the electron can attain quasi-periodic motions, oscillating between the impurity and a small region of the lattice. This region corresponds to the center of a localized state in the lattice with an energy matched by that of the impurity. By precisely tuning the impurity energy, the electron can be set to oscillate between the impurity and a region far from the impurity, even distances larger than the Anderson localization length. The electron oscillations result from the interference of hybrized states, which have some resemblance to Pendry's necklace states [J. B. Pendry, J. Phys. C: Solid State Phys. 20, 733-742 (1987)]. The dependence of the electron motion on the impurity energy gives a potential mechanism for selectively routing an electron towards different regions of a 1D disordered lattice. * for the electron. Necklace states also exist in optical systems [22,23]. These states form a sub-band that can induce resonant transport similar to the energy band of an ordered lattice. Resonances of finite disordered systems coupled to infinite reservoirs have been theoretically studied in [24,25].Extrapolating from these previous studies, here we consider finite disordered lattices (or quantum wires) with a side-attached impurity ("T-junction"). The impurity can be realized using a quantum dot, which constitutes a nano-control device. The properties of the dot can be altered through a gate potential allowing an experimentalist control over electron transport. Varying the gate potential on the dot can be used to probe the spectrum and localization properties of the lattice. As we will show, we can indeed use an impurity to direct transport within a disordered lattice. In our theoretical study we will consider the case of zero temperature. Therefore the transport we will discuss is different from variable-range hopping [26,27], which occurs at non-zero temperature. We will discuss possible extension of our work to the case of nonzero temperature in section VIII. Note that our lattice is finite, but large enough so that boundary effects only play a minor role.Experimentally, effective 1-D systems can be synthesized by a variety of techniques [28,29], including lattice geometries that incorporate a side-attached quantum dot [30,31]. Randomized site potentials in a finite lattice might be obtained, for example, by varying segment lengths (i.e., growth times) in GaAs/GaP superlattices assembled by laser-assisted catalytic growth [15,29]. An arXiv:1511.08758v2 [cond-mat.mes-hall]

New deep learning models are massively over-parametrized, e.g., GPT-3 and Turing-NLG exceed 100Bs of parameters. Naturally, model reduction techniques such as pruning, quantization, and distillation have been proposed and deployed. In the pruning literature, the Lottery Ticket Hypothesis (LTH) is amongst the most cited. LTH provides a recipe for reducing the free parameters of a deep network by eliminating a large fraction of its edges by 1) remembering and reusing only the edges on the highest-traffic input-output paths and 2) resetting remaining parameters to their initial values after each round of elimination. Here, we extend this idea two steps further. We add a random buildup phase, starting from a small percentage of parameters to reach a predefined accuracy, often needing fewer than 50% of the parameters of a full network. Then we eliminate parameters using an LTH-like procedure combined with a binary search. We demonstrate the efficiency of the proposed technique using three well-known image data sets by sparsifying three standard deep nets. We exceed the elimination power of LTH (over 98% pruned) and effectively match the performance of full networks. We conclude that for both reducing computation and maintaining a sparse network for inference, the proposed scheme is effective and practical.

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