Abstract
The quantum dynamics of a localized spin\(-\frac {1}{2} \) Particle interacting with an absorbing environment is investigated. The quantum Langevin-Schrödinger equation for spin\(-\frac {1}{2} \) is obtained. The susceptibility function of the environment is calculated in terms of the coupling function of the spin and the environment. it is shown that the susceptibility function satisfies the Kramers-Kronig relations. Spontaneous emission and the shift frequency of the spin is obtained in terms of the imaginary part of the susceptibility function in frequency domain. Some transition probabilities between the spin states are calculated when the absorbing environment is in the thermal state.
Similar content being viewed by others
References
Messer, J.: Acta phys. Austriaca 50, 75 (1979)
Dekker, H.: phys. Rep. 80, 1 (1981)
Haken, H.: Rev. Mod. Phys. 47, 67 (1975)
Kheirandish, F., Amooshahi, M.: Int. Theor. Phys. 45, 1 (2006)
Kheirandish, F., Amooshahi, M.: Mod. Phys. Lett. A 20(39), 3025 (2005)
Bateman, H.: Phys. Rev. 38, 815 (1931)
Kanai, E.: Prog. Theoret. Phys. 440, 3 (2948)
Callen, H., Welton, T.: Phys. Rev. 83, 34 (1951)
Weber, J.: Phys. Rev. 90, 977 (1953)
Feynman, R.P., Vemon, F.L.: Ann. Phys. 24, 118 (1963)
Messer, J.: Math. Phys. 2, 281 (1978)
Caldetra, A., Legget, A.: Physica. A 121, 587 (1983)
Caldeira, A., Legget, A.: Phys. Rev. A 31, 1059 (1985)
Celeghini, E., Rasseti, M., Vitello, G.: Ann. Phys. 215, 156 (1992)
Brittin, W.E.: Phys. Rev. 77, 396 (1950)
Senitzky, I.R.: Phys. Rev. 119, 970 (1960)
Svinin, I.R.: Theor. Mat. Fiz. 27, 2037 (1972)
Havas, P.: Bull. Am. Phys. Soc. 1, 337 (1956)
Valentini, G.: Rend. 1st. Lomb. So: A 95, 255 (1961)
Razavy, M.: Can. J. Phys. 50, 2037 (1972)
Hung, M.C., Wu, M.C.: Chin. J. Phys. 36(4) (1998)
Lopez, G., Gonzalez, G.: Int. J. Theor. Phys. 43, 10 (2004)
Haken, H.: Rev. Mod. Phys. 47, 67 (1975)
Berman, G.P., Borgonovi, F., Lopez, G.V., Tsifrinnovich, V.I.: Phys. Rev. A 68, 012102 (2003)
Caldeira, A.O., Legget, A.J.: Phys. Rev. Lett. 46, 211 (1981)
Caldeira, A.O., Legget, A.J.: Ann. Phys. 149, 374 (1983)
Unruh, W.G., Zurek, W.H.: Phys. Rev. D 40, 1071 (1989)
Hu, B.L., Paz, J.P., Zhang, Y.: Phys. Rev. D 45, 2843 (1992)
Smith, C.M., Caldeira, A.O.: Phys. Rev. A 36, 3509 (1987)
Ford, G.W., Kac, M., Mazur, P.: J. Math. Phys. 6(4) (1964)
Castro, A.H., Caldeira, A.O.: Phys. Rev. Lett. 67, 1960 (1991)
Ford, G.W., Lewis, J.T., Oconell, R.F.: Phys. Rev. A 37, 4419 (1987)
Jackson, J.D.: Classical electrodynamics. John Wiley (1998)
Scully, M.O., Zubairy, M.S.: Quantum optic. Cambridge (1997)
Milonni, P.W.: The quantum vacuum. Academic Press (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Amooshahi, M. Spin\(-\frac {1}{2}\) Particle in an Absorbing Environment. Int J Theor Phys 54, 3691–3698 (2015). https://doi.org/10.1007/s10773-015-2605-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-015-2605-3