1. On the Mourre estimates for Floquet Hamiltonians
- Author
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Amane Kiyose and Tadayoshi Adachi
- Subjects
Physics ,Floquet theory ,Mourre estimates ,Floquet Hamiltonians ,010102 general mathematics ,Statistical and Nonlinear Physics ,01 natural sciences ,Schrödinger operator with time-periodic potentials ,symbols.namesake ,AC Stark Hamiltonians ,0103 physical sciences ,symbols ,010307 mathematical physics ,Scattering theory ,0101 mathematics ,Hamiltonian (quantum mechanics) ,Mathematical Physics ,Schrödinger's cat ,Mathematical physics - Abstract
In the spectral and scattering theory for a Schrodinger 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.
- Published
- 2019
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