T-matrix formalism for one space dimension systems with different spatial asymptotics and symmetry relations for ferromagnetic Josephson junctions

摘要

We present a study of quantum scattering systems in one space dimension with different spatial asymptotics on the left and right, using as a specific model a ferromagnetic Josephson junction with inhomogeneous magnetization texture. So except for the space dimension there is also a particle-hole and a spin degree of freedom. We focus on the stationary scattering states of such systems and derive appropriate Lippmann-Schwinger equations for them. These lead us to define a channel-dependent T-matrix, as in N-body multichannel scattering theory, where the role of the channels is played by the different asymptotic Hamiltonians and indicates an appropriate temporal evolution. The channel-dependent T-matrix elements are shown to be proportional to the scattering amplitudes and this fact is used to obtain symmetry conditions for them, under the action of anti-unitary transformations. We then present some of the consequences of our findings to the current-phase-relation of ferromagnetic Josephson junctions, the spectrum of Andreev bound states and a simplification of the Furusaki-Tsukada formula for the dc Josephson current.