Translation Representations and Scattering By Two Intervals
Spectral Theory
2015-06-03 v1 Quantum Physics
Abstract
Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U (t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator, and scattering matrix. We illustrate our results in the Lax-Phillips model where (U (t), H) represents an acoustic wave equation in an exterior domain; and in quantum tunneling for dynamics of quantum states.
Keywords
Cite
@article{arxiv.1201.1447,
title = {Translation Representations and Scattering By Two Intervals},
author = {Palle Jorgensen and Steen Pedersen and Feng Tian},
journal= {arXiv preprint arXiv:1201.1447},
year = {2015}
}