Localization of the number of photons of ground states in nonrelativistic QED

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 self-adjoint operator acting on $\LR\otimes\fff\cong L^2(\BR;\fff)$, 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 number operator of $\fff$. Moreover it is shown that, for almost every electron position variable $x\in\BR$ and for arbitrary $k\ge 0$, $\|(1\otimes \N)\gr (x) \|_\fff \leq D_ke^{-δ|x|^{m+1}}$ with some constants $m\ge 0$, $D_k>0$, and $\delta >0$ independent of $k$. In particular $\gr\in \cap_{k=1}^\infty D (e^{β|x|^{m+1}}\otimes N^k)$ for $0<\beta <\delta /2$ is obtained.

43pages

References in corpus (3)

• Ground States in Non-relativistic Quantum Electrodynamics
• Enhanced Binding in non-relativistic QED
• Infrared regular representation of the three dimensional massless Nelson model

Cited by in corpus (5)

• Spectral Renormalization Group and Local Decay in the Standard Model of the Non-relativistic Quantum Electrodynamics
• Continuity properties of the semi-group and its integral kernel in non-relativistic QED
• Ionisation by quantised electromagnetic fields: The photoelectric effect
• Ground state photon number at large distance
• Stochastic differential equations for models of non-relativistic matter interacting with quantized radiation fields