Semigroup Decoherence

• The toy model H0=0 (still no unitary evolution):

  • ?(x,x',t) = ?(x,x',0) exp(– [?W(x') –?W(x)]2 t)

• If x=x' or W(x) = W(x') then

  • ?(x,x',t) = ?(x,x',0):
    • no diagonal decoherence,
    • no decoherence where W(x) is constant

• If W(x) ? W(x') then

  • ?(x,x',t) ? 0:
    • off-diagonal decoherence where W(x) varies.

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