Stefan Teufel, Herbert Spohn
Semi-classical motion of dressed electrons
(92K, Latex2e)
ABSTRACT. We consider an electron coupled to the quantized radiation field and
subject to a slowly varying electrostatic potential. We establish that
over sufficiently long times radiation effects are negligible and the
dressed electron is governed by an effective one-particle Hamiltonian.
In the proof only a few generic properties of the full Pauli-Fierz
Hamiltonian $H_{\rm PF}$ enter. Most importantly, $H_{\rm PF}$ must
have an isolated ground state band for $|p|< p_{\rm c}\leq \infty$ with
$p$ the total momentum and $p_{\rm c}$ indicating that the ground state
band may terminate. This structure demands a local approximation
theorem, in the sense that the one-particle approximation holds until
the semi-classical dynamics violates $|p|