Journal article
Translation representations and scattering by two intervals
Journal of Mathematical Physics, Vol.53(5), pp.053505-053505-49
2012
DOI: 10.1063/1.4709770
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.
Details
- Title: Subtitle
- Translation representations and scattering by two intervals
- Creators
- Palle JorgensenSteen PedersenFeng Tian
- Resource Type
- Journal article
- Publication Details
- Journal of Mathematical Physics, Vol.53(5), pp.053505-053505-49
- DOI
- 10.1063/1.4709770
- ISSN
- 0022-2488
- eISSN
- 1089-7658
- Language
- English
- Date published
- 2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983985926902771
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