Random magnetic field and quasi-particle transports in the mixed state of high T_(c) cuprates

By a singular gauge transformation, the quasi-particle transport in the mixed state of high T_{c} cuprates is mapped into charge-neutral composite Dirac fermion moving in short-range correlated random scalar and long-range correlated vector potential. A fully quantum mechanical approach to longitudinal and transverse thermal conductivities is presented. The semi-classical Volovik effect is presented in a quantum mechanical way. The quasi-particle scattering from the random magnetic field which was completely missed in all the previous semi-classical approaches is the dominant scattering mechanism at sufficiant high magnetic field. The implications for experiments are discussed.