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A Model to Describe Transport Properties in $Bi_2Sr_2(Ca_zPr_{1-z})Cu_2O_{8+y}$

A pseudo-spin model is proposed, as a means to describe some transport properties (resistivity and Hall mobility) in $Bi_2Sr_2(Ca_zPr_{1-z})Cu_2O_{8+y}$. Our model is based in a double-well potential where tunneling in a given site and interaction between different lattice sites are allowed only through the excited states. Doping of the pure system by the addition of $Pr$ increases the ratio between the activation energy and the tunneling constant. The model Hamiltonian displays some features which are present in the hydrogen-bonded ferroelectrics. Its dynamics is treated in the random phase approximation and the characteristic frequency (time) is used in a Drude formula in order to obtain some transport properties of the system, namely the electric resistivity and the Hall mobility. The quantities calculated in this work are compared with the experimental data of B. Beschoten, S. Sadewasser, G. Güntherodt and C. Quitmann [Phys. Rev. Lett.77, 1837(1996)].