Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wave Operators and Similarity for Long Range $N$-body Schr\"odinger
  Operators   We consider asymptotic behavior of $e^{-itH}f$ for $N$-body Schr\"odinger
operator $H=H_0+\sum_{1\le i<j\le N}V_{ij}(x)$ with long- and short-range pair
potentials $V_{ij}(x)=V_{ij}^L(x)+V_{ij}^S(x)$ $(x\in {\mathbb R}^\nu)$ such
that $\partial_x^\alpha V_{ij}^L(x)=O(|x|^{-\delta-|\alpha|})$ and
$V_{ij}^S(x)=O(|x|^{-1-\delta})$ $(|x|\to\infty)$ with $\delta>0$. Introducing
the concept of scattering spaces which classify the initial states $f$
according to the asymptotic behavior of the evolution $e^{-itH}f$, 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 $\delta>1/2$ by using this
decomposition theorem under some assumption on subsystem eigenfunctions.

25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph