LOWER SPECTRAL BRANCHES OF A PARTICLE COUPLED TO A BOSE FIELD
Résumé
The structure of the lower part (i.e. $\varepsilon $-away below the two-boson threshold) spectrum of Fröhlich's polaron Hamiltonian in the weak coupling regime is obtained in spatial dimension $d\geq 3$. It contains a single polaron branch defined for total momentum $p\in G^{\left( 0\right) } $, where $G^{\left( 0\right) }\subset {\mathbb R}^d$ is a bounded domain, and, for any $p\in {\mathbb R}^d$, a manifold of polaron + one-boson states with boson momentum $q$ in a bounded domain depending on $p$. The polaron becomes unstable and dissolves into the one boson manifold at the boundary of $G^{\left( 0\right) }$. The dispersion laws and generalized eigenfunctions are calculated.
Domaines
Physique mathématique [math-ph]
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