A method for the study of spatially non-homogeneous quasiparticle and phonon distributions

Based on investigations in the field of non-equilibrium superconductivity, namely the simulation of a special type of X-ray detectors (superconducting tunnel junction detectors), we developed a new approach for the study of non-equilibrium phenomena governed by quantum mechanical Boltzmann equations. The method, called pseudolinearization, is particularly useful if the diffusion takes place on a time scale that is much larger than that of the particle–particle interactions. Then, the simulation of diffusion and the interaction processes can be decoupled, and the problem is reduced to the calculation of stationary solutions of a system of integro-differential equations and the simulation of a diffusion process. Our method provides a fast and reliable tool to evaluate such stationary solutions. We discuss the application of pseudolinearization for different temperatures below Tc and for various superconducting materials.