#master equation

[lookatphysics]

Master equation

Replaced PPTX, more explicit derivation, new script, 7m18s, watched in entirety on udemy (thus vimeo), spotchecked on YouTube

2012 Aug 23 22h34 EDT Recorded a rescripted version (to go with an edited PPTX) that edits down to 7m19s.  100% uploaded at 22h37 EDT.  Email from vimeo at 22h40 EDT indicating conversion complete, available for viewing.  Chose different thumbnail. Refetched on udemy at 22h34 EDT to update length (reads out as 7m20s on udemy/vimeo).  

2012 Aug 23 23h16 EDT After watching on udemy, edited a grammatical error (subject-verb number agreement) around 4m27s.  100% uploaded by 23h17 EDT.  Length slightly shorter (still rounds to 7m19s).  Email from vimeo at 22h20 EDT indicating conversion complete, video available for viewing.  Still reports 7m20s on vimeo.  

2012 Aug 24 00h58 EDT After watching yet again on udemy, edited a mathematical logic error (referred to finite {\Delta}P when in fact {\Delta}P could be zero).  Dropped this adjective.  Video still rounds to 7m19s in Camtasia (7m18s plus change now instead of 7m19s plus change).  Windows explorer calls it 7m18s.  Upload tx rate fluctuating a lot from 10-s period to 10-s period.  Restarting upload (got stuck at 68%).  This is more consistently decent.  100% uploaded at 01h06 EDT.  Email from vimeo at 01h08 EDT indicating conversion complete and video available for viewing.  Vimeo reads out the length as 7m19s.  Refetched to udemy at 01h12 EDT.  

2012 Aug 24 07h45 EDT Watched in entirety rescripted/rePPTXed master equation on udemy (thus vimeo).  Fine.  Leave alone.  

2012 Aug 24 07h49 EDT Replaced "draft video" icon on lookatphysics.com with "video" icon.  

2012 Aug 24 07h52 Replaced older 2012-0421 SSA Master Equation.pptx with newest 2012-0823 SSA Master Equation.pptx on lookatphysics.com

2012 Aug 24 10h45 EDT Spotchecked on YouTube (beginning + a couple places, beginning and one of the places after were to check audio splicing).  Looks fine.  

[whordijk-blog]

Bachelor Thesis finished

Just before Christmas I finished and defended my Bachelor Thesis. It was graded with 8.5 out of 10 points.

This thesis describes the process of deriving the Master Equation for the time evolution of the density operator for a lead coupled spinless Hubbard chain using a Markov approximation. The derivation is done in a direct, conventional way of expanding operators and switching pictures in order to separate the system Hamiltonian in a convenient way and through the Super Operator formalism, yielding a different form of the Master Equation. We will implement both results in software and we will iteratively find the stationary state of the chain from some initial state when the lead is kept at a constant chemical potential. We will show that for each initial state the chain density operator converges to this stationary state that is determined by the chemical potential of the lead, but at a rate that is independent of the chemical potential of the lead and that both the conventional and the Super Operator approach yield the exact same results. We will also show and discuss a small systematic error we find in the converged results yielding non-physical interpretations and how we can improve the numerics regarding the implementation of the model.