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We discuss the phenomenology of the superconductivity resulting from the bose condensation of the preformed pairs coexisting with unpaired fermions. We show that this transition is more mean field like than usual bose condensation, i.e. it is characterized by a relatively small value of the Ginzburg parameter. We consider the Hall effect in the vortex flow regime and in the fluctuational regime above Tc and show that in this situation it is much less than in the transition driven entirely by bose condesation but much larger than in a usual superconductivity. We analyse the available Hall data and conclude that this phenomenology describes reasonably well the data in the underdoped materials of Y BaCuO family but is not an appropriate description of optimally doped materials or underdoped LaSrCuO.

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We reformulate the two-channel Kondo model to explicitly remove the unscattered charge degrees of freedom. This procedure permits us to move the non-Fermi liquid xed point to in nite coupling where we can apply a perturbative strong-coupling expansion. The xed point Hamiltonian involves a three-body Majorana zero mode whose scattering e ects give rise to marginal self-energies. The compacti ed model is the N = 3 member of a family of \O(N)" Kondo models that can be solved by semiclassical methods in the large N limit. For odd N, fermionic \Kink" uctuations about the N = 1 mean-eld theory generate a fermionic N-body bound-state which asymptotically decouples at low energies. For N = 3, our semi-classical methods fully recover the non-Fermi liquid physics of the original two channel model. Using the same methods, we nd that the corresponding O (3) Kondo lattice model develops a spin-gap and a gapless band of coherently propagating three-body bound-states. Its strong-coupling limit o ers a rather interesting realization of marginal Fermi liquid.72.15. Nj, 71.30+h,