Simple semiconductor electron conductance simulator using MERW: Maximal Entropy Random Walk (available code) 1

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1. 

   Wikipedia about MERW: https://en.wikipedia.org/wiki/Maximal_entropy_random_walk

   Full article (MERW introduction) with the animation above (made in Mathematica, source available in the article): https://community.wolfram.com/groups/-/m/t/2924355

   **Animation shows density evolution** (injecting single electron in the starting point, what is the probability distribution for finding it after increasing numbers of steps) – naive random walk (GRW: uniform probability among outgoing edges) vs MERW (maximizing mean entropy) on rectangular lattice with defects – randomly removed some edges … as simple model of electron conductance in semiconductor (lattice of silicon atoms with dopants as defects).

   GRW leads to nearly uniform stationary probability distribution – incorrectly predicting it to be a conductor.

   In contrast, **MERW predicts stationary probability distribution exactly as quantum mechanics**, with **strong localization** ( https://en.wikipedia.org/wiki/Anderson_localization
   ) – preventing conductance … also leading to **short circuits: current localizing in narrow paths of least resistance**.

   Working MERW diode model as p-n junction: https://arxiv.org/pdf/2112.12557

   jarekduda

   May 29, 2023

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