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Approximate gap equation

  1. Mar 15, 2014 #1
    The superconduction gap equation is:

    1=VN(0)arsinh(ωD/lΔl).

    My book says that in the weak coupling limit VN(0)<<1 this will reduce to:

    lΔl = ωDexp(-1/VN(0))

    But how is this obtained. We have:

    arsinh(ωD/lΔl) = ln(ωD2+√(ωD2 + lΔl2)), but what has the approximation of this got to do with the prefactor being small? Also I don't see how you get a negative exponent?
     
  2. jcsd
  3. Mar 15, 2014 #2

    tiny-tim

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    hi aaaa202! :smile:
    erm :redface: … 

    first write it ωD/lΔl = sinh(1/VN(0)) :wink:
     
  4. Mar 15, 2014 #3
    wow lol.. thanks
     
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