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Dissipative Scalar Field Theory: A Covariant Formulation

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Abstract

Caldeira-Leggett model of reservoir is generalized to a reservoir modeled by a continuum of real Klein-Gordon fields, instead of harmonic oscillators. A quantum Langevin type dissipative equation is obtained for the scalar field. The susceptibility of the medium is defined in terms of the reservoir Green’s function and the coupling function satisfying causality condition. The connection between the coupling function and the susceptibility of the medium is found to be a Hankel transform from which the coupling function can be determined in terms of the susceptibility of the medium. Noise currents and their fluctuation-dissipation relation are obtained. In a homogeneous medium or reservoir, explicit form of the quantum scalar field, and its large-time limit, are found.

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References

  1. Dalvit, D.A.R., Milonni, P.W., Roberts, D.C. Rosa, F.S.S. (ed.): Lecture Notes in Physics 834, p.345. Springer-Verlag (2011)

  2. Guth, A.H.: Phys. Rev. D23, 347 (1981)

    ADS  Google Scholar 

  3. Brandenberger: Rev. Mod. Phys. 57, 1 (1985)

    Article  ADS  Google Scholar 

  4. Huttner, B., Barnett, S.M.: Phys. Rev. A46, 4306 (1992)

    Article  ADS  Google Scholar 

  5. Kheirandish, F., Soltani, M.: Phys. Rev. A78, 012102 (2008)

  6. Kheirandish, F., Jaffari, M.: Phys. Rev. A86, 022503 (2012)

    Article  ADS  Google Scholar 

  7. Kheirandish, F., Soltani, M., Jafari, M.: Phys. Rev. A84, 062120 (2011)

    Article  ADS  Google Scholar 

  8. Amooshahi, M.: Eur. Phys. J. D54, 115 (2009)

    ADS  Google Scholar 

  9. Caldeira, A.O., Leggett, A.J.: Phys. Rev. Lett. 46(211) (1981)

  10. Caldeira, A.O., Leggett, A.J.: Ann. Phys. 149(374) (1983)

  11. Caldeira, A.O., Leggett, A.J.: Physica 121A, 587 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  12. Weiss, U.: Quantum Dissipative Systems (1993, World Scientific) and the references therein

  13. Voss, R.F., Webb, R.A.: Phys. Rev. Lett. 47, 265 (1981)

    Article  ADS  Google Scholar 

  14. Martinis, J.M., Devoret, M.H., Clarke, J.: Phys. Rev. Lett. 55, 1543 (1985)

    Article  ADS  Google Scholar 

  15. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic, New York (2007)

    MATH  Google Scholar 

  16. Amooghorban, E., Kheirandish, F.: Int. J. Theor. Phys. 53, 2593–2615 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kheirandish, F., Amooshahi, A.: Mod. Phys. Lett. A 20(39), 3025–3034 (2005)

    Article  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Sanandaj branch, Islamic Azad University, Sanandaj, Iran

    A. Refaei

  2. Department of Physics, Faculty of Science, The University of Isfahan, Isfahan, Iran

    F. Kheirandish

Authors
  1. A. Refaei
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  2. F. Kheirandish
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Correspondence to F. Kheirandish.

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Refaei, A., Kheirandish, F. Dissipative Scalar Field Theory: A Covariant Formulation. Int J Theor Phys 55, 432–439 (2016). https://doi.org/10.1007/s10773-015-2677-0

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  • DOI: https://doi.org/10.1007/s10773-015-2677-0

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