Effects of Disorder on Electron Transport in Arrays of Quantum Dots

We investigate the zero-temperature transport of electrons in a model of quantum dot arrays with a disordered background potential. One effect of the disorder is that conduction through the array is possible only for voltages across the array that exceed a critical voltage $V_T$. We investigate the behavior of arrays in three voltage regimes: below, at and above the critical voltage. For voltages less than $V_T$, we find that the features of the invasion of charge onto the array depend on whether the dots have uniform or varying capacitances. We compute the first conduction path at voltages just above $V_T$ using a transfer-matrix style algorithm. It can be used to elucidate the important energy and length scales. We find that the geometrical structure of the first conducting path is essentially unaffected by the addition of capacitive or tunneling resistance disorder. We also investigate the effects of this added disorder to transport further above the threshold. We use finite size scaling analysis to explore the nonlinear current-voltage relationship near $V_T$. The scaling of the current $I$ near $V_T$, $I\sim(V-V_T)^{\beta}$, gives similar values for the effective exponent $\beta$ for all varieties of tunneling and capacitive disorder, when the current is computed for voltages within a few percent of threshold. We do note that the value of $\beta$ near the transition is not converged at this distance from threshold and difficulties in obtaining its value in the $V\searrow V_T$ limit

Understanding ML driven HPC: Applications and Infrastructure

We recently outlined the vision of "Learning Everywhere" which captures the possibility and impact of how learning methods and traditional HPC methods can be coupled together. A primary driver of such coupling is the promise that Machine Learning (ML) will give major performance improvements for traditional HPC simulations. Motivated by this potential, the ML around HPC class of integration is of particular significance. In a related follow-up paper, we provided an initial taxonomy for integrating learning around HPC methods. In this paper, which is part of the Learning Everywhere series, we discuss "how" learning methods and HPC simulations are being integrated to enhance effective performance of computations. This paper identifies several modes --- substitution, assimilation, and control, in which learning methods integrate with HPC simulations and provide representative applications in each mode. This paper discusses some open research questions and we hope will motivate and clear the ground for MLaroundHPC benchmarks.Comment: Invited talk to "Visionary Track" at IEEE eScience 2019. arXiv admin note: text overlap with arXiv:1806.04731 by other author