# The Library

### Effective density of states for a quantum oscillator coupled to a photon field

Tools

Betz, Volker and Castrigiano, Domenico P. L..
(2011)
*Effective density of states for a quantum oscillator coupled to a photon field.*
Communications in Mathematical Physics, Volume 301
(Number 3).
pp. 811-839.
ISSN 0010-3616

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1007/s00220-010-1167-8

## Abstract

We give an explicit formula for the effective partition function of a harmonically bound particle minimally coupled to a photon field in the dipole approximation. The effective partition function is shown to be the Laplace transform of a positive Borel measure, the effective measure of states. The absolutely continuous part of the latter allows for an analytic continuation, the singularities of which give rise to resonances. We give the precise location of these singularities, and show that they are well approximated by first order poles with residues equal to the multiplicities of the corresponding eigenspaces of the uncoupled quantum oscillator. Thus we obtain a complete analytic description of the natural line spectrum of the charged oscillator.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QC Physics |

Divisions: | Faculty of Science > Mathematics |

Library of Congress Subject Headings (LCSH): | Harmonic oscillators, Quantum field theory, Hamiltonian systems |

Journal or Publication Title: | Communications in Mathematical Physics |

Publisher: | Springer |

ISSN: | 0010-3616 |

Date: | 2011 |

Volume: | Volume 301 |

Number: | Number 3 |

Page Range: | pp. 811-839 |

Identification Number: | 10.1007/s00220-010-1167-8 |

Status: | Peer Reviewed |

Publication Status: | Published |

Funder: | Engineering and Physical Sciences Research Council (EPSRC) |

Grant number: | EP/D07181X/1 (EPSRC) |

References: | 1. Bach, V., Fröhlich, J., Sigal, I.M.: Quantum Electrodynamics of Conﬁned Nonrelativistic Particles. Adv. in Math. 137, 299–395 (1998) 2. Bach, V., Fröhlich, J., Sigal, I.M.: Return to Equilibrium. J. Math. Phys. 41, 3985–4060 (2000) 3. Betz, V., Hiroshima, F., L˝orinczi, J., Minlos, R.A., Spohn, H.: Ground state properties of the Nelson Hamiltonian - A Gibbs measure-based approach. Rev. Math. Phys. 14, 173–198 (2002) 4. Castrigiano, D.P.L., Kokiantonis, N.: Quantum oscillator in a non-self-interacting radiation ﬁeld: Exact calculation of the partition function. Phys. Rev. A 35(10), 4122–4128 (1987) 5. Castrigiano, D.P.L., Kokiantonis, N., Stiersdorfer, H.: Natural Spectrum of a Charged Quantum Oscillator. Il Nuovo Cimento 108(7), 765–777 (1993) 6. Cohen-Tannoudji, C., Dupont-Roc, J., Grynberg, G.: Photons and Atoms. New York: John Wiley, 1987 7. Cohen-Tannoudji, C., Dupont-Roc, J., Grynberg, G.: Atom-Photon Interactions. New York: John Wiley, 1998 8. Feynman, R.P.: Statistical Mechanics.Reading, MA: Benjamin, 1972 9. Griesemer, M., Lieb, E., Loss, M.: Ground states in non-relativistic quantum electrodynamics. Invent. Math. 145(3), 557–595 (2001) 10. Hiroshima, F., Spohn, H.: Enhanced binding through coupling to a quantum ﬁeld. Ann. Henri Poincaré 2, 1159–1187 (2001) 11. Hunziker, W.: Resonances, Metastable States and Exponential Decay Laws in Perturbation Theory. Commun. Math. Phys. 132, 177–188 (1990) 12. Kirsch, W., Metzger, B.: The integrated density of states for random Schrödinger operators. Proc. Symp. in Pure Math. 76(2), 649 (2007) 13. Louisell, W.H.: Quantum Statistical Properties of Radiation. New York: John Wiley, 1973, Chap. 5, and D. Marcuse: Principles of Quantum Electronics, London-New York: Academic Press, 1980, Chap. 5 14. Merkli, M., Sigal, I.M., Berman, G.P.: Decoherence and thermalization. Phys. Rev. Lett.98, 130401 (2007) 15. Merkli, M., Sigal, I.M., Berman, G.P.: Resonance theory of decoherence and thermalization. Ann. Phys. 323, 373–412 (2009) 16. Reed, M., Simon, B.: Methods of Modern Mathematical Physics IV: Analysis of Operators. New York: Academic Press, 1978 17. Simon, B.: Functional Integration and Quantum Physics. New York: Academic Press, 1979 18. Spohn, H.: Dynamics of charged particles and their radiation ﬁelds. Cambridge: Cambridge University Press, 2004 19. Weidmann, J.: Linear Operators in Hilbert Spaces. Berlin-Heidelberg-New York: Springer, 1980 |

URI: | http://wrap.warwick.ac.uk/id/eprint/41674 |

Data sourced from Thomson Reuters' Web of Knowledge

### Actions (login required)

View Item |