 02498 Fumio Hiroshima
 Photon number localization of ground states in nonrelativistic QED
(80K, latex)
Nov 30, 02

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Abstract. One electron system minimally coupled to a quantized radiation field
is considered.
It is assumed that the quantized radiation field is {\it massless}, and
{\it no} infrared cutoff is imposed.
The Hamiltonian, $H$, of this system
is defined as a selfadjoint operator acting on
$\LR\otimes\fff$, where $\fff$ is the Boson Fock space over $L^2(\BR\times\{1,2\})$.
It is shown that
the ground state, $\gr$, of $H$ belongs to
$\cap_{k=1}^\infty D(1\otimes N^k)$,
where $N$ denotes the photon number operator of $\fff$.
Moreover it is shown that,
for almost every electron position variable $x\in\BR$ and for arbitrary $k\geq 0$,
$\(1\otimes \N)\gr (x) \_\fff \leq
D_ke^{\delta x^{m+1}}$ with some constants $m$, $D_k$, and $\delta$
independent of $k$.
In particular $\gr\in \cap_{k=1}^\infty
D (e^{\beta x^{m+1}}\otimes N^k)$ for
$0<\beta<\delta/2$ is obtained.
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