On the Absence of Excited Eigenstates of Atoms in QED
Tóm tắt
For the standard model of QED with static nuclei, nonrelativistic electrons and an ultraviolet cutoff, a new simple proof of absence of excited eigenstates with energies above the groundstate energy and below the ionization threshold of an atom is presented. Our proof is based on a multi-scale virial argument and exploits the fact that, in perturbation theory, excited atomic states decay by emission of one or two photons. Our arguments do not require an infrared cutoff (or regularization) and are applicable for all energies above the groundstate energy, except in a small (α-dependent) interval around the ionization threshold.
Tài liệu tham khảo
Bach V., Fröhlich J., Pizzo A.: Infrared-Finite Algorithms in QED I. The Groundstate of an Atom Interacting with the Quantized Radiation Field. Commun. Math. Phys. 264(1), 145–165 (2006)
Bach V., Fröhlich J., Sigal I.M.: Renormalization group analysis of spectral problems in quantum field theory. Adv. in Math. 137, 205–298 (1998)
Bach V., Fröhlich J., Sigal I.M.: Spectral analysis for systems of atoms and molecules coupled to the quantized radiation field. Commun. Math. Phys. 207(2), 249–290 (1999)
Bach V., Fröhlich J., Sigal I.M., Soffer A.: Positive commutators and the spectrum of Pauli-Fierz Hamiltonian of atoms and molecules. Commun. Math. Phys. 207(3), 557–587 (1999)
Delone N.B., Goreslavsky S.P., Krainov V.P.: Dipole matrix elements in the quasi-classical approximation. J. Phys. B: At. Mol. Opt. Phys. 27, 4403–4419 (1994)
Derezinski J., Jaksic V.: Spectral theory of Pauli-Fierz operators. J. Func. Anal. 180(2), 243–327 (2001)
Derezinski J., Gerard C.: Asymptotic completeness in quantum field theory. Massive Pauli-Fierz Hamiltonians. Rev. Math. Phys. 11(4), 383–450 (1999)
Fröhlich J., Griesemer M., Schlein B.: Asymptotic completeness for Rayleigh scattering. Ann. H. Poincaré 3, 107–170 (2002)
Fröhlich, J., Griesemer, M., Sigal, I.M.: Mourre estimate and spectral theory for the standard model of non-relativistic QED. http://www.ma.utexas.edu/mp-arc/index-06.html, 06-316, 2006
Georgescu V., Gerard C., Moller J.S.: Spectral theory of massless Pauli-Fierz models. Commun. Math. Phys. 249(1), 29–78 (2004)
Gerard, C.: A proof of the abstract limiting absorption principle by energy estimates. http://www.ma.utexas.edu/mp-arc/index-07.html, 07-43, 2007
Griesemer M.: Exponential decay and ionization threshold in non-relativistic quantum electrodynamics. J. Funct. Anal. 210(3), 321–340 (2004)
Griesemer M., Lieb E., Loss M.: Ground states in non-relativistic quantum electrodynamics. Invent. math. 145(3), 557–595 (2001)
Hubner M., Spohn H.: Spectral model of the spin-boson Hamiltonian. Ann. Inst. H. Poincare Phys. Theor. 62(3), 289–323 (1995)
Matsumoto A.: Multipole matrix elements for hydrogen atom. Physica Scripta 44, 154–157 (1991)
Reed M., Simon B.: Methods of modern mathematical physics. IV. Analysis of operators. Academic Press, New York (1978)
Sahbani J.: The conjugate operator method for locally regular Hamiltonians. J. Operator Theory 38(2), 297–322 (1997)
Skibsted E.: Spectral analysis of N-body systems coupled to a bosonic field. Rev. Math. Phys. 10(7), 989–1026 (1998)