Lower Spectral Branches of a Particle Coupled to a Bose Field

Details Lower Spectral Branches of a Particle Coupled to a Bose Field Lower Spectral Branches of a Particle Coupled to a Bose Field

2005-05-03

arxiv.org/abs/math-ph/0505009v1

Physics

Mathematical Physics

Scientific paper

10.1142/S0129055X05002509

The structure of the lower part (i.e. $\epsilon $-away below the two-boson threshold) spectrum of Fr\"ohlich'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^{(0)} $, where $G^{(0)}\subset {\mathbb R}^d$ 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 $G^{(0)}$. The dispersion laws and generalized eigenfunctions are calculated.

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