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arXiv · 1201.1447

Translation Representations and Scattering By Two Intervals

Palle Jorgensen·Steen Pedersen·Feng Tian
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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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Palle Jorgensen, Steen Pedersen, Feng Tian. 2012-01-06. Translation Representations and Scattering By Two Intervals. https://doi.org/10.1063/1.4709770

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