Multichanel localization and magnetic impurities

The behaviour of an electron in N-coupled conducting chains of the length L is studied in the presence of magnetic impurities. The electron flow can be expanded in an orthonormal set of 2N channels. Each channel has its own transmission coefficient T_n(L). Spontaneous breaking of the symmetry between channels results in 2N different exponential dependences T_n(L) ～ exp (—L/l¹_n) where l¹_n is a localization length in the nth channel. Low frequency kinetic behaviour depends on the channel with the maximum localization length l¹₀.