Transport Equation in Transverse Magnetic Fields: Magnetoresistance and Thermopower in Metals

A transport equation is derived for a quantum mechanical system in a transverse magnetic field. The solution to this equation gives the linear transport coefficients for electrostatic fields and temperature gradients for electrons in metals. In term of a small expansion parameter, the solution to lowest order confirms the existing semiclassical theory on electrical conductivity and thermal conductivity. We also found that the electron phonon mass enhancement factor is present in the adiabatic thermopower. The next higher order approximation exhibits the anisotropic effect caused by the presence of magnetic fields, and explains the experimentally observed linear magnetoresistance in simple metals at high magnetic field.