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The second order co-tunneling rate can be calculated analytically for zero temperature.
Starting from (2.44) for N=2, the co-tunneling rate may be written as
F Second Order Co Tunneling Rate at Zero Temperature
At zero temperature the Fermi functions are either zero or one and may
therefore be moved in the boundaries of the integrals.
The integration over
is eliminated by the -function.
demanded by the
-function and the integration regions of
for the new upper boundaries of integration.
The integrand can be changed to a partial sum
And finally collecting the logarithms yields