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Quantum Transport by Yaroslav M. Blanter, Yuli V. Nazarov

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4 Randomness and interference

This chapter treats quantum interference effects in disordered conductors. We have already discussed interference phenomena for the few-channels case in Section 1.6, and in Chapter 2 we have seen that the scattering approach becomes increasingly complicated for many transport channels. This is why we need special methods to treat many-channel diffusive conductors. Some of their properties can be understood if we replace the Hamiltonian or a scattering matrix by a random matrix. In Section 4.1 we discuss random matrices as mathematical objects and review the properties of their eigenvalues and eigenvectors. We then use random matrix theory to describe the properties of energy levels (Section 4.2) and transmission ...

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