New simulator for electron conductance in quantum scale
Jarek Duda
edge is equally probable, doesn’t really maximize entropy as
mathematics expects from thermodynamical models, but do it only
locally.
Such models lead to Brownian motion in continuous limit, which is good
enough approximation to model diffusion in fluids, but isn’t longer
appropriate within fixed structure of solids, like for recently
measured electron stationary probability density on a defected lattice
of potential wells of semiconductor surface:
http://physicsworld.com/cws/article/news/41659
We would rather say that this probability density is quantum
mechanical ground state ... but this sample is macroscopic, so we
should expect to see some current flow behind – some thermodynamical
behavior of these 'quants of charge'.
It occurs that when we use stochastic model which finally do what
mathematics expects from us – really maximize entropy, we get going to
exactly quantum mechanical ground state stationary probability
density, like we would thermodynamically expect from quantum
mechanics.
So maybe starting from such models we could better understand dynamics
of current flow in quantum scale...
I’ve just made Mathematica demonstration which allow to compare
electron conductance through defected lattice using both – based on
standard Generic Random Walk (classical) and these new models based on
Maximal Entropy Random Walk.
It allows to observe both stationary probability distribution and
dynamics of current flow for different defect densities and applied
potential gradient:
http://demonstrations.wolfram.com/preview.html?draft/93373/000008/ElectronConductanceModelUsingMaximalEntropyRandomWalk
or
https://docs.google.com/leaf?id=0B7ppK4IyMhisMTRiNGZjYWItMDU0NS00OTFjLTg0NmQtOWE4ZTg5ZTkzMTJk&hl=en
They give completely different qualitative picture – I would like to
ask which of them better correspond to conductance at quantum level?
And generally I would be grateful for any remarks and comments about
the demonstration.