SPECTRAL ASYMPTOTICS FOR MAGNETIC SCHRODINGER OPERATOR WITH SLOWLY VARYING POTENTIAL

被引：0

作者：

Dimassi, Mouez ^{[1
]}

Yazbek, Hawraa ^{[1
]}

Watanabe, Takuya ^{[2
]}

机构：

[1] Univ Bordeaux, IMB, UMR 5251, CNRS, 351 Cours Liberat, F-33405 Talence, France

[2] Ritsumeikan Univ, 1-1-1 Noji Higashi, Kusatsu 5258577, Japan

来源：

OSAKA JOURNAL OF MATHEMATICS | 2023年 / 60卷 / 03期

关键词：

SHIFT FUNCTION; TRACE FORMULA; STRIP; RESONANCES; SYSTEMS; FIELD;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the Schrodinger operator with constant magnetic field and smooth potential V : H(epsilon) = H + V(epsilon x, epsilon y), H = D-x(2) + (D-y + mu x)(2), (x, y) is an element of Omega(d), with Dirichlet boundary conditions. Here Omega(d) = Pi(d)(j=1)] - a(j), a(j)[xR(y)(d). The spectral properties of two operators H and H(epsilon) are investigated. For epsilon small enough, we study the effect of the slowly varying potential V(epsilon x, epsilon y). In particular, we derive asymptotic trace formula and we give an asymptotic expansion in powers of epsilon of the spectral shift function corresponding to (H(epsilon), H).

引用

页码：709 / 731

页数：23

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