 00396 Stefan Teufel, Herbert Spohn
 Semiclassical motion of dressed electrons
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Oct 5, 00

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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 oneparticle Hamiltonian.
In the proof only a few generic properties of the full PauliFierz
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 oneparticle approximation holds until
the semiclassical dynamics violates $p<p_{\rm c}$. Within this
framework we prove an abstract Hilbert space theorem which uses no
additional information on the Hamiltonian away from the band of
interest. Our result is applicable to other timedependent semi
classical problems. We discuss semiclassical distributions for the
effective oneparticle dynamics and show how they can be translated to
the full dynamics by our results.
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