Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0511094

Effects of Disorder on Electron Transport in Arrays of Quantum Dots

Shantenu Jha·A. Alan Middleton
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 $V_T$, $I\sim(V-V_T)^β$, gives similar values for the effective exponent $β$ 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 $β$ near the transition is not converged at this distance from threshold and difficulties in obtaining its value in the $V\searrow V_T$ limit.

Explore related subjects

cond-mat.dis-nn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Shantenu Jha, A. Alan Middleton. 2005-11-04. Effects of Disorder on Electron Transport in Arrays of Quantum Dots. https://arxiv.org/abs/cond-mat/0511094

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Deep-layered machines have a built-in Occam's razor

Many complex systems map vast numbers of microscopic descriptions onto far fewer macroscopic outcomes. Surprisingly, these input-output maps strongly favor simple outputs. In an exactly solvable deep-layered machine, we prove that simplicity bias strengthens with every layer. The probability of an output function $F$ approaches $\Pr(F)\propto 2^{-K(F)}$, where $K$ is the Kolmogorov complexity. Our results show that hierarchical composition alone can generate an intrinsic Occam's razor, suggesting a general mechanism for simplicity bias in learning and evolution.

cond-mat.dis-nn↗
arXiv2026

Neural Networks with Exciton-Polariton Waveguides

We propose and numerically study a scheme for neural networks using exciton-polariton waveguide meshes. These enable arbitrary programmable interlayer couplings suited to a restricted Boltzmann machine architecture where polariton phases act as stochastic network variables. We show that such a network can be trained using unsupervised Hebbian and anti-Hebbian updates. This allows the implementation of an associative memory, where the network recovers learned patterns from imperfect inputs.

cond-mat.dis-nn↗
arXiv2026

Finite-width shift of the edge of chaos in deep neural networks

Deep neural networks train best when they are initialised at the edge of chaos, the critical line in the plane of weight and bias variances on which the distance between two inputs neither grows nor shrinks with depth. The line is known for infinitely wide networks; at finite width it moves, and how it moves has been disputed. We treat the logarithm of the distance between two inputs through a network of width $N$ as a random walk and compute its drift and variance to order $1/N$. The edge of chaos moves to a larger weight variance, by $Δσ_w^2=-a_1/(N\,\partial_{σ_w^2}\lnχ_1)$, about $8/N$ for $\tanh$ networks at a bias variance of $0.05$, confirmed by simulations of the exact finite-width recursion. The shift describes a typical network; the average over many networks is dominated by rare networks in which the distance grows, and its critical point moves the other way, which explains why calculations and simulations have disagreed. Backpropagation follows the same random walk, so the shift applies to gradients unchanged. Along the edge of chaos, the information about the similarity of two inputs is constant until the compression over the depth exceeds about one nat, which fixes where to sit on the line. The results give an initialisation rule, Crinit, that places a network on its finite-width edge of chaos without a search. On MNIST and Fashion-MNIST at width $64$ it is more accurate than the standard rules at their usual settings, by a small margin in shallow networks and a large one in deep networks, where most standard rules fail; it trains in fewer steps, and it matches or beats the standard rules with a tuned gain.

cond-mat.dis-nn↗