From: jos.bergervoet@xs4all.nl   
      
   On 21/02/10 7:31 PM, p.kinsler@ic.ac.uk wrote:   
   > Jos Bergervoet  wrote:   
   >>> And here is the meaning of all transformations   
   >>> being the outcome of QM tunneling.  Is tunneling always   
   >>> probalistic or is it sometimes an analytic function.   
   >   
   >> Neither. It is *always* an analytical function! The wavefunction   
   >> gradually changes from one which only has a high amplitude in one   
   >> region to one with the high amplitude in the other region (at the   
   >> other side of the barrier). There is nothing probabilistic about   
   >> that, not even in the most hard-core Copenhagen picture.   
   >   
   > What sorts of things are called "tunneling" is often a matter   
   > of usage; and my experience differs. Whilst doing my PhD,   
   > for example, I had cause to make a clear distinction between   
   > "coherent tunneling" of the kind you describe, and other   
   > tunneling between two states, which *was* statistical,   
      
   I'm pretty sure you cannot prove that!   
      
   > and   
   > driven by quantum noise (see e.g. doi:10.1103/PhysRevA.40.4813   
   > or doi:10.1103/PhysRevA.43.6194).   
      
   Then the question is which things you call "quantum noise". if   
   you just mean all the degrees of freedom of the surroundings   
   then it is still deterministic quantum mechanical time evolution,   
   so that is not what I would call statistical. Likewise, if it is   
   determined by very fine details of the initial state then it is   
   again not statistical, at least not in the "playing with dice"   
   sense. Those things are merely intractable (and of course in   
   that sense can be called statistical).   
      
   So did you have proof that there exist cases where tunneling   
   (or anything that happens to a quantum state) can *not* be   
   explained by the initial state and the coupling to surroundings?   
      
   > Now it might be that you are horrified that such processes   
   > could be called "quantum tunneling", but to people working   
   > in the area, it was unremarkable. Not all terminology is   
   > always used in the same way.   
      
   Still I don't think this is just a discussion about terminology.   
   It's the old question whether QM is deterministic or not! And   
   if you can give proof that it isn't, I won't be too horrified,   
   just very surprised. Actually, the deterministic aspect is of   
   course horrifying in its own way.. :-)   
      
   >   
   > #Paul   
      
   --   
   Jos   
      
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