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On the Mourre estimates for Floquet Hamiltonians

  • Tadayoshi AdachiEmail author
  • Amane Kiyose
Article

Abstract

In the spectral and scattering theory for a Schrödinger operator with a time-periodic potential \(H(t)=p^2/2+V(t,x)\), the Floquet Hamiltonian \(K=-i\partial _t+H(t)\) associated with H(t) plays an important role frequently, by virtue of the Howland–Yajima method. In this paper, we introduce a new conjugate operator for K in the standard Mourre theory, that is different from the one due to Yokoyama, in order to relax a certain smoothness condition on V.

Keywords

Mourre estimates Floquet Hamiltonians Schrödinger operator with time-periodic potentials AC Stark Hamiltonians 

Mathematics Subject Classification

81U05 81Q10 

Notes

Acknowledgements

The first author is partially supported by the Grant-in-Aid for Scientific Research (C) #17K05319 from JSPS. The authors are grateful to the referees for many valuable comments and suggestions.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Course of Mathematical Science, Department of Human Coexistence, Graduate School of Human and Environmental StudiesKyoto UniversityKyoto-shiJapan
  2. 2.Department of Mathematics, Graduate School of ScienceKobe UniversityKobe-shiJapan

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