Do the Profile Function singularities explain the high energy reflection of fermions in a phase transition?

Abstract

We investigate the scope of a previous result concerning the behaviour of fermions hitting a general wall caused by a first-order phase transition. The wall profile function was considered to be analytic in the real axis. The previous result is valid for analytic functions in the whole complex plane except in certain isolated singularities located out of the real axis. A non-analytic profile function in the real axis is studied in order to show the validity of the result for any profile which can be put as a certain limit of a function which verifies the latter. A new understanding of the high energy behaviour of the quantum reflection caused by a sharp profile, as the step, arises from that study.