On the Mourre estimates for three-body Floquet Hamiltonians

Abstract

In this paper,we consider the Floquet Hamiltonian $K$ associated with a three-body Schrödinger operator with time-periodic pair potentials $H(t)$. By introducing a conjugate operator $A$ for $K$ in the standard Mourre theory, we prove the Mourre estimate for $K$. As by-products of the Mourre estimate for $K$, the minimal velocity estimates for the physical propagator $U(t,0)$ generated by $H(t)$ as well as the propagator $e^{-i\sigma K}$ generated by $K$ can be obtained.

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