A time-independent approach for the study of the spectral shift function and an application to Stark Hamiltonians
A time-independent approach for the study of the spectral shift function and an application to Stark Hamiltonians
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用于研究谱位移函数的与时间无关的方法及其在斯塔克哈密顿量中的应用
DOI：
10.1080/03605302.2015.1053567
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发表时间：
2015
影响因子：
1.9
通讯作者：
Mouez DIMASSI and Setsuro FUJIIE
中科院分区：
文献类型：
--
作者：
K. Kuto;Y. Miyamoto;T. Mori;T. Tsujikawa and S. Yotsutani;Mouez DIMASSI and Setsuro FUJIIE
本文发展了一种与时间无关的谱移函数研究方法。我们应用这种方法的扰动斯塔克哈密顿量。得到了算子对（P=P0+V（x），P0= −h2Δ +x1），x=（x1，..，xn）的SSF的弱渐近性和Weyl型渐近性，其中V（x）∈H ∞（H ∞，H ∞）在无穷远处衰减得足够快，且是一个小的正参数.在非俘获能λ附近，给出了SSF导数的h次方的逐点渐近展开式，并显式计算了两个前导项.
In this paper we develop a time-independent approach for the study of the spectral shift function (SSF for short). We apply this method for the perturbed Stark Hamiltonian. We obtain a weak and a Weyl-type asymptotics with optimal remainder estimate of the SSF of the operator pair (P=P0+V(x),P0= −h2Δ +x1),x= (x1,…,xn) whereV(x) ∈ 𝒞∞(ℝn, ℝ) decays sufficiently fast at infinity, andhis a small positive parameter. Near a non-trapping energy λ, we give a pointwise asymptotic expansions in powers ofhof the derivative of the SSF, and we compute explicitly the two leading terms.