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approach arbitrarily large radius Área de Publicações atom-electromagnetic field system behaviour Brasileiro de Pesquisas Cauchy theorem cavity Centro Brasileiro coefficients Cohen-Tannoudji confined problem continuous formalism coordinates q coordinates q'0 corresponding coupled system coupling constant coupling oscillator-field decoherence defined describing the system dressed atom Dressed configurations dressed coordinates dressed mechanical oscillator Ecole Normale Superieure eigenfrequencies eigenstates electromagnetic field equations of motion evaluate exact field modes finite free space Hamiltonian harmonic modes Haroche idea of dressed initial condition mathematical matrix elements modes Fourier components neighbourhood rj non-perturbative normal collective normal modes Fourier Nrj2 obtain orthonormal matrix oscillator and field oscillator frequency oscillator q oscillator-field system perturbation theory Pesquisas Físicas Área point of view principal axis quadratic form quantities describing refs right hand term Rio de Janeiro scalar field sphere of radius strong coupling system composed system confined taking the limit transformation matrix valid for weak weak coupling Xavier Sigaud