Electron conductance model using Maximal Entropy Random Walk
To emphasize some scenarios in thermodynamical models, we assign energy to each of them and instead of assuming uniform probability distribution, we use Boltzmann distribution which is some compromise between maximizing entropy and minimizing energy.
To express stronger walker’s tendency for jumping in given direction for conductance models, we introduce a (fixed) difference of potential energy between succeeding layers of the defected lattice.
We can use Boltzmann distribution in generally two ways now: locally - for each vertex among its outgoing edges (natural expansion of GRW), or globally - among whole paths (MERW analogue).
The controls allows to choose applicated potential gradient (), edge removal probability from regular 2D lattice ), the size of lattice () and the number of considered pseudorandom scenario (). The ‘’ button allows to turn on/off cyclical boundary conditions in vertical direction.
The ‘’ button allows to switch between observing stationary probability density and dynamics of current flow. By clicking on the picture we can choose the point in which the current is injected.
To find more informations about characteristic for quantum mechanics localization properties finally observed in random walk, see http://link.aps.org/doi/10.1103/PhysRevLett.102.160602
"Electron conductance model using Maximal Entropy Random Walk" from The Wolfram Demonstrations Project
Contributed by: Jarek Duda