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Open Quantum Systems Decoherence Quantum Simulation Entanglement Theory Quantum Correlations

Wave Operators and Similarity for Long Range N-body Schrödinger Operators

arXiv
Authors: Hitoshi Kitada

Year

2015

Paper ID

26116

Status

Preprint

Abstract Read

~2 min

Abstract Words

136

Citations

N/A

Abstract

We consider asymptotic behavior of e-itHf for N-body Schrödinger operator H=H0+sum1le i<jle NVij(x) with long- and short-range pair potentials Vij(x)=VijL(x)+VijS(x) \(xin {mathbb R}^ν\) such that partialx^αVijL(x)=O\(|x|-δ-|α|\) and VijS(x)=O\(|x|-1-δ\) \(|x|→infty\) with δ>0. Introducing the concept of scattering spaces which classify the initial states f according to the asymptotic behavior of the evolution e-itHf, we give a generalized decomposition theorem of the continuous spectral subspace {mathcal{H}}c(H) of H. The asymptotic completeness of wave operators is proved for some long-range pair potentials with δ>1/2 by using this decomposition theorem under some assumption on subsystem eigenfunctions.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • We consider asymptotic behavior of e^-itHf for N-body Schrödinger operator H=H0+sum1le i infty) with δ>0.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1511.05137 [2] arXiv https://arxiv.org/abs/1511.05137 [3] Publisher https://arxiv.org/abs/1511.05137

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