Form factors of local operators in a one-dimensional two-component Bose gas

Overview & Synopsis

We consider physical interpretations of non-trivial boundary conditions of self-adjoint extensions for one-dimensional Schr\"odinger operator of freespinless particle. Despite its model and rather abstract character this question is worth of investigation due to application for one-dimensionalnanostructures. The main result is the physical interpretation of peculiar self-adjoint extension with discontinuity of both the probability density andthe derivative of the wave function. We show that this case differs very much from other three which were considered before and corresponds to the presence of mass-jump in a sense of works of Ganella et. al., (Journal of Physics A: Mathematical and Theoretical 42, 465207 (2009)) along with the quantized magnetic flux. Real physical system which can be modeled by such boundary conditions is the localized quantazied flux in the Josephson junction of two superconductors with different effective masses of the elementary excitations.