2010年3月

# Scattering theory for two-body quantum systems with singular potentials in a time-periodic electric field

JOURNAL OF MATHEMATICAL PHYSICS
• ,
• Toshiyuki Kimura
• ,
• Yoshimasa Shimizu

51
3

032103 (23pp)

DOI
10.1063/1.3317902

AMER INST PHYSICS

Recently, the first author [Adachi, "Asymptotic completeness for N-body quantum systems with long-range interactions in a time-periodic electric field," Commun. Math. Phys. 275, 443 (2007)] proved the asymptotic completeness for N-body quantum systems with long-range interactions in a time-periodic electric field whose mean in time is nonzero by obtaining propagation estimates for the physical propagator. However, in his work, it is needed that potentials under consideration are sufficiently smooth. In this paper, when N=2, we prove the asymptotic completeness of (modified) wave operators under the assumption that the potential has the local singularity of type vertical bar x vertical bar(-1+epsilon) when d &gt;= 3 and 0 &lt;epsilon &lt; 1, where d is the space dimension. We also discuss the modifiers in the position representation, which are used in the definition of the modified wave operators in the long-range case.

Web of Science ® 被引用回数 : 2

リンク情報
DOI
https://doi.org/10.1063/1.3317902
Web of Science