1 research outputs found
Scattering Theory and -Symmetry
We outline a global approach to scattering theory in one dimension that
allows for the description of a large class of scattering systems and their
-, -, and -symmetries. In
particular, we review various relevant concepts such as Jost solutions,
transfer and scattering matrices, reciprocity principle, unidirectional
reflection and invisibility, and spectral singularities. We discuss in some
detail the mathematical conditions that imply or forbid reciprocal
transmission, reciprocal reflection, and the presence of spectral singularities
and their time-reversal. We also derive generalized unitarity relations for
time-reversal-invariant and -symmetric scattering
systems, and explore the consequences of breaking them. The results reported
here apply to the scattering systems defined by a real or complex local
potential as well as those determined by energy-dependent potentials, nonlocal
potentials, and general point interactions.Comment: Slightly expanded revised version, 38 page