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Translation representations and scattering by two intervals
Journal article   Peer reviewed

Translation representations and scattering by two intervals

Palle Jorgensen, Steen Pedersen and Feng Tian
Journal of Mathematical Physics, Vol.53(5), pp.053505-053505-49
2012
DOI: 10.1063/1.4709770
url
https://arxiv.org/pdf/1201.1447View
Open Access

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.

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