Particle production and effective thermalization in inhomogeneous mean field theory

Gert Aarts; Jan Smit

doi:10.1103/PhysRevD.61.025002

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Particle production and effective thermalization in inhomogeneous mean field theory

Gert Aarts¹ and Jan Smit^1,2

¹Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlands
²Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, the Netherlands

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Phys. Rev. D 61, 025002 – Published 16 December, 1999

DOI: https://doi.org/10.1103/PhysRevD.61.025002

Abstract

As a toy model for dynamics in nonequilibrium quantum field theory we consider the Abelian Higgs model in $1 + 1$ dimensions with fermions. In the approximate dynamical equations, inhomogeneous classical (mean) Bose fields are coupled to quantized fermion fields, which are treated with a mode function expansion. The effective equations of motion imply e.g. Coulomb scattering, due to the inhomogeneous gauge field. The equations are solved numerically. We define time dependent fermion particle numbers with the help of the single-time Wigner function and study particle production starting from inhomogeneous initial conditions. The particle numbers are compared with the Fermi-Dirac distribution parametrized by a time dependent temperature and chemical potential. We find that the fermions approximately thermalize locally in time.

References (18)

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[c1] F. Cooper, S. Habib, Y. Kluger, E. Mottola, J. P. Paz, and P. R. Anderson, Phys. Rev. D 50, 2848 (1994).

[c2] Y. Kluger, J. M. Eisenberg, B. Svetitsky, F. Cooper, and E. Mottola, Phys. Rev. Lett. 67, 2427 (1991); F. Cooper, S. Habib, Y. Kluger, and E. Mottola, Phys. Rev. D 55, 6471 (1997).

[c3] D. Boyanovsky, H. J. de Vega, R. Holman, and J. F. J. Salgado, Phys. Rev. D 54, 7570 (1996); ibid.D. Boyanovsky, D. Cormier, H. de Vega, R. Holman, A. Singh, and M. Srednicki, 56, 1939 (1997).

[c4] D. Boyanovsky, C. Destri, H. J. de Vega, R. Holman, and J. Salgado, Phys. Rev. D 57, 7388 (1998).

[c5] Y. Kluger, J. M. Eisenberg, B. Svetitsky, F. Cooper, and E. Mottola, Phys. Rev. D 45, 4659 (1992).

[c6] D. Boyanovsky, M. D’Attanasio, H. J. de Vega, R. Holman, and D. S. Lee, Phys. Rev. D 52, 6805 (1995); ibid.J. Baacke, K. Heitmann, and C. Pätzold, 58, 125013 (1998).

[c7] G. Aarts and J. Smit, Nucl. Phys. B555, 355 (1999).

[c8] L. M. A. Bettencourt and C. Wetterich, Phys. Lett. B 430, 140 (1998).

[c9] D. Y. Grigoriev and V. A. Rubakov, Nucl. Phys. B299, 67 (1988).

[c10] S. Y. Khlebnikov and I. I. Tkachev, Phys. Rev. Lett. 77, 219 (1996).

[c11] For recent reviews, see e.g., V. A. Rubakov and M. E. Shaposhnikov, Usp. Fiz. Nauk 166, 493 (1996); M. Trodden, hep-ph/9803479.

[c12] J. García-Bellido, D. Grigoriev, A. Kusenko, and M. Shaposhnikov, Phys. Rev. D 60, 123504 (1999).

[c13] P. B. Greene and L. Kofman, Phys. Lett. B 448, 6 (1999); G. F. Giudice, M. Peloso, A. Riotto, and I. Tkachev, J. High Energy Phys. 08, 014 (1999).

[c14] L. Kofman, A. Linde, and A. A. Starobinsky, Phys. Rev. D 56, 3258 (1997).

[c15] D. Vasak, M. Gyulassy, and H. T. Elze, Ann. Phys. (N.Y.) 173, 462 (1987).

[c16] J. P. Blaizot and E. Iancu, Nucl. Phys. B390, 589 (1993); Phys. Rev. Lett. 70, 3376 (1993); Nucl. Phys. B417, 608 (1994).

[c17] P. Zhuang and U. Heinz, Ann. Phys. (N.Y.) 245, 311 (1996); ibid.S. Ochs and U. Heinz, 266, 351 (1998).

[c18] D. Ibaceta and E. Calzetta, Phys. Rev. E 60, 2999 (1999).

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Particle production and effective thermalization in inhomogeneous mean field theory

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