Maximal Entropy Random Walk: repairing diffusion-QM disagreement

Abstract: Considering diffusion or chaos in [0,1] range leads to uniform stationary probability distribution rho=1. In contrast, QM predicts localized rho~sin^2 there. This disagreement is crucial e.g. for semiconductors – standard diffusion would predict nearly uniform electron distribution, allowing them to flow – incorrectly expecting it to be a conductor. In contrast, QM predicts strong e.g. Anderson localization preventing conductance.

Maximal Entropy Random Walk (MERW) allows to understand and repair this disagreement - turns out that standard random walk often only approximates the (Jaynes) principle of maximal entropy, which is crucial for statistical physics models – MERW is the most random among random walk, thanks of it leading to stationary probability distribution exactly as quantum ground state – with localization property. In contrast to standard random walk, MERW is also scale-free, time symmetric and nonlocal. It also has many other applications (~160 citations).

mathematical physicsgeneral physicsquantum physics

Audience: general audience

( paper | slides )

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QM Foundations & Nature of Time seminar

Series comments: Description: Physics foundations discussion seminar

Current access link in th.if.uj.edu.pl/~dudaj/QMFNoT

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