# On the Mourre estimates for three-body Floquet Hamiltonians

## TL;DR

This paper establishes Mourre estimates for three-body Floquet Hamiltonians with time-periodic potentials, advancing spectral analysis techniques for such quantum systems.

## Contribution

The paper introduces a conjugate operator within Mourre theory to prove spectral estimates for three-body Floquet Hamiltonians with time-periodic interactions.

## Key findings

- Proved Mourre estimate for the Floquet Hamiltonian K.
- Extended Mourre theory to three-body time-periodic systems.
- Provided spectral analysis tools for Floquet Hamiltonians.

## Abstract

In this paper, we consider the Floquet Hamiltonian $K$ associated with a three-body Schr\"odinger 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 $K$.