On the Mourre estimates for Floquet Hamiltonians
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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.
KeywordsMourre estimates Floquet Hamiltonians Schrödinger operator with time-periodic potentials AC Stark Hamiltonians
Mathematics Subject Classification81U05 81Q10
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.
- 3.Adachi, T.: On the Mourre estimates for three-body Floquet Hamiltonians, preprint. arXiv:1904.10190