Semiclassical approximation of the magnetic Schrödinger operator on a strip: dynamics and spectrum
作者: Mouez Dimassi
刊名: Tunisian Journal of Mathematics, 2020, Vol.2 (1), pp.197-215
来源数据库: Project Euclid
DOI: 10.2140/tunis.2020.2.197
关键词: Semiclassical analysisPeriodic Schrödinger operatorBohr–Sommerfeld quantizationSpectral shift functionAsymptotic expansionsLimiting absorption theorem
原始语种摘要: In the semiclassical regime (i.e., ϵ ↘ 0 ), we study the effect of a slowly varying potential V ( ϵ t , ϵ z ) on the magnetic Schrödinger operator P = D x 2 + ( D z + μ x ) 2 on a strip [ − a , a ] × ℝ z . The potential V ( t , z ) is assumed to be smooth. We derive the semiclassical dynamics and we describe the asymptotic structure of the spectrum and the resonances of the operator P + V ( ϵ t , ϵ z ) for ϵ small enough. All our results depend on the eigenvalues corresponding to D x 2 + ( μ x + k ) 2 on L 2 ( [ − a , a ] ) with Dirichlet boundary condition.
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关键词翻译
关键词翻译
  • operator 话务员
  • dinger 铁道终点站站长
  • spectrum 光谱
  • semiclassical 半经典的
  • dynamics 动力学
  • approximation 近似
  • absorption 吸收
  • potential 
  • magnetic 磁的
  • quantization 量子化