Semi-classical motion of dressed electrons

Details Semi-classical motion of dressed electrons Semi-classical motion of dressed electrons

2000-10-05

arxiv.org/abs/math-ph/0010009v2

Physics

Mathematical Physics

Latex2e, 32 pages. Statement and proof of Lemma 11 clarified

Scientific paper

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_PF enter. Most importantly, H_PF must have an isolated ground state band for |p| < p_c <= \infty with p the total momentum and p_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|

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