Renormalized wave equation for an electron coupled to thermodynamic fluctuations of magnetization

We derive the wave equation for an electron coupled via the $s-d$ interaction to a system of magnetically disordered spins at nonzero temperature. A nonlinear Schrödinger equation is derived for the case of spins undergoing the Gaussian fluctuations. It shows that the character of the wave function may be significantly modified by a thermal disorder, leading to self-trapped and spin-split states in a paramagnetic medium.