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Long-time behavior of an electron interacting with a quantized radiation field
| Title: | Long-time behavior of an electron interacting with a quantized radiation field |
| Authors: | Arai, Asao Browse this author →KAKEN DB |
| Keywords: | electrons | | radiations | | quantization | | coupling | | ground states | | equilibrium | | quantum electrodynamics | | photons | | dipole approximation | | temperature distribution | | displacements | | boltzmann constant | | effective mass | | renormalization |
| Issue Date: | Aug-1991 |
| Publisher: | American Institute of Physics |
| Journal Title: | Journal of Mathematical Physics |
| Volume: | 32 |
| Issue: | 8 |
| Start Page: | 2224 |
| End Page: | 2242 |
| Publisher DOI: | 10.1063/1.529197 |
| Abstract: | The long-time behavior of an electron coupled to a quantized radiation field is discussed in the ground state and in equilibrium states at finite temperatures. The electron is not confined in an external potential. The model used is a d-dimensional extension of a standard model (the Pauli–Fierz model) in nonrelativistic quantum electrodynamics: The electron moves in R^d (d=>2) and the radiation field is over R^d. Further, the energy function ω of one free photon is taken to be a general one. In defining the interaction part of the Hamiltonian of the model, an ultraviolet cutoff is introduced for photon momenta with a cutoff function ρ-hat and the dipole approximation is used. It is proved that at each finite temperature T>0, the mean-square displacement of the electron behaves like (kBTd/m)t^2 as time t tends to infinity, where kB is the Boltzmann constant and m>0 is a renormalized mass of the electron which should be identified with the observed mass of the electron. The long-time asymptotics of the mean square displacement of the electron in the ground state is different from that at the finite temperatures; it depends on the space dimension d and on the infrared behavior of ω and ρ-hat. |
| Rights: | Copyright © 1991 American Institute of Physics |
| Relation: | http://www.aip.org/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/13674 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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