Energy transport in strongly disordered superconductors and magnets

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A more detailed discussion experimental implications will be published separately (M. V. Feigel’man, L.B. Ioffe and M. Mézard, in preparation)

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The situation is very different in Josephson arrays and granular films which display very different phenomenology fn00

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The use of the mean field approximation in the cavity mapping is very different from its use in ( 2

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The “temperature” of the DP is here equal to 1 1 and has nothing to do with the inverse temeprature β \beta of the spin problem

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When some of the energy denominators get small, they are regularized to ( ω − 2 ​ ξ n ) 2 + ( g / K ) 2 (\omega-2\xi_{n})^{2}+(g/K)^{2} . This can be shown by noticing that at most one neighbor of a given spin has a small energy denominator. This reduces the problem to a 1D spin chain in which individual ξ \xi are distributed with the probabilty density K K around ω / 2 \omega/2 which can be mapped onto non-interacting fermions

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