Abstract
Zurek's and Kibble's causal constraints for defect production at continuous transitions are encoded in the field equations that condensed matter systems and quantum fields satisfy. In this article we highlight some of the properties of the solutions to the equations and show to what extent they support the original ideas.
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REFERENCES
W.H. Zurek, Physics Reports 276,Number 4, November 1996.
W.H. Zurek, Nature 382, 297 (1996), P. Laguna and W.H. Zurek, Phys. Rev. Lett. 78, 2519 (1997). A. Yates and W.H. Zurek, Phys. Rev. Lett. 80 5477 (1998)
N.D. Antunes, L.M.A. Bettencourt, W.H. Zurek, Phys. Rev. Lett. 82, 2824 (1999).
W.H. Zurek, Nature 317, 505 (1985), Acta Physica Polonica B24, 1301 (1993).
T.W.B. Kibble, J. Phys. A9, 1387 (1976).
T.W.B. Kibble, in Common Trends in Particle and Condensed Matter Physics, Physics Reports 67, 183 (1980).
T.W.B. Kibble, talk presented at the Meeting on Monopoles in Quantum Field Theory at ICTP, Trieste, December 1991 (Imperial College preprint)
T.W.B. Kibble, Acta Physica Polonica B13, 723 (1982)
R.H. Brandenberger and J. Maguiejo, e-print astro-ph/0002030. Lecture notes of the International School on Cosmology, Kish Island, Iran, Jan. 22–Feb. 4 1999, to be publ. in “Large Scale Structure Formation” (Kluwer, Dordrecht, 2001)
T.W.B. Kibble and E.J. Weinberg, Phys. Rev. D81, 3188 (1991)
V.M.H. Ruutu et al., Nature 382, 334 (1996).
C. Bauerle et al., Nature 382, 332 (1996).
E. Kavoussanaki, R. Monaco and R.J. Rivers, Phys. Rev. Lett. 81, 3452 (2000)
M.E. Dodd et al., Phys. Rev. Lett. 81, 3703 (1998), J. Low Temp. Physics 15, 89 (1999).
M.M. Salomaa and G.E. Volovik, Rev. Mod. Phys. 59, 533 (1987), G.E. Volovik, Physics Reports, to be published (e-print cond-mat/0007361).
A. Vilenkin and E.P.S. Shellard, Cosmic Strings and Other Topological Defects, (CUP, 1994) M.B. Hindmarsh and T.W.B. Kibble, Cosmic Strings, Reports. Prog. Phys. 58,477 (1995)
H. Kleinert, Gauge Fields in Condensed Matter (World Scientific, Singapore, 1989) Vol. 1.
T.W.B. Kibble and G.E. Volovik, Pis'ma v ZhETF 65, 96 (1997)
I.S. Aranson, N.B. Kopnin and V.M. Vinokur, preprint cond-mat/9905286
J.R. Anglin and W.H. Zurek, Phys. Rev. Lett. 83, 1707 (1999)
C. Greiner and B. Muller, Phys. Rev. D55, 1026 (1997)
F. Lombardo and F.D. Mazzitelli, Phys. Rev. D53, 2001 (1996)
T. Vachasparti and A. Vilenkin, Phys. Rev. D30, 2036 (1984), R.J. Scherrer and A. Vilenkin, Phys. Rev. D56 647 (1997); Phys. Rev. D58 103501 (1998)
J. Robinson and A. Yates, Phys. Rev. D54 5211 (1996)
B.I. Halperin, published in Physics of Defects, proceedings of Les Houches, Session XXXV 1980 NATO ASI, editors Balian, Kléman and Poirier (North-Holland Press, 1981) p.816.
F. Liu and G.F. Mazenko, Phys. Rev. B46, 5963 (1992).
D. Ibaceta and E. Calzetta, Phys. Rev. E60, 2999 (1999).
V.N. Popov Functional integrals and collective excitations, Cambridge University Press (1997), Chapter 8.
M. Gleiser and H-R. Muller, Phys. Lett. B422 69 (1998)
D. Ibaceta, E. Calzetta, Phys. Rev. E60, 2999 (1999)
E. Kavoussanaki, R.J. Rivers and G. Karra, Condensed Matter Physics 3, 133 (2000).
R.J. Rivers and E. Kavoussanaki, e-print cond-mat/9901348
Yu. M. Bunkov and O.D. Timofeevskaya, Phys. Rev. Lett. 80, 4927 (1998).
G. Karra and R.J. Rivers, Phys. Rev. Lett. 81, 3707 (1998).
R.J. Rivers, Phys. Rev. Lett. 84, 1248 (2000).
P. Laguna and W.H. Zurek Phys. Rev. D 58, 085002 (1998)
D. Boyanovsky, Da-Shin Lee and A. Singh, Phys. Rev. D48, 800 (1993), D. Boyanovsky, H.J. de Vega, and R. Holman, Phys. Rev. D49, 2769 (1994); D. Boyanovsky, H.J. de Vega, R. Holman, D.-S. Lee, and A. Singh, Phys. Rev. D51, 4419 (1995); D. Boyanovsky, D. Cormier, H.J. de Vega, R. Holman, and S. Prem Kumar, Phys. Rev. D57, 2166 (1998)
D. Boyanovsky, H.J. de Vega and R. Holman, published in Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions, proceedings of Les Houches, 1999 NATO ASI (Vol. 549), editors Y.M. Bunkov and H. Godfrin (Kluwer Academic Publishers, Dordrecht, 2000), p.139.
G. Karra and R. J. Rivers, Physics Letters B414, 28 (1997)
L.M.A. Bettencourt, N.D. Antunes and W.H. Zurek, Phys. Rev. 62, 065005 (2000)
L.M.A. Bettencourt, e-print hep-ph/0005264
M. Bowick and A. Momen, Phys. Rev. D58, 085014 (1998)
F. Cooper, S. Habib, Y. Kluger, E. Mottola Phys. Rev. D55 (1997) 6471 (1997) F. Cooper, S. Habib, Y. Kluger, E. Mottola, J. P. Paz, and P. R. Anderson, Phys. Rev. D50 2848 (1994)
F.C. Lombardo, F.D. Mazzitelli, and R.J. Rivers, e-print hep-ph/0102152, and work in preparation.
G.J. Stephens, E.A. Calzetta, B-L Hu, S.A. Ramsey, Phys. Rev. D59, 045009 (1999)
R. Feynman and F. Vernon, Ann. Phys. (N. Y.) 24, 118 (1963)
A. Guth and S-Y. Pi, Phys. Rev. D32, 1899 (1985). O. Eboli, R. Jackiw and S-Y. Pi, Phys. Rev. D37, 3557 (1988).
S.P. Kim and C.H. Lee, hep-ph/0011227
A.J. Gill and R.J. Rivers, Phys. Rev. D51, 6949 (1995)
M. Gleiser and R.O. Ramos, Phys. Rev. D50, 2441 (1994); A. Berera, M. Gleiser, R. O. Ramos Phys. Rev. D58, 123508 (1998)
P.C. Hendry et al, Nature 368, 315 (1994).
W.F. Vinen, Proc. Roy. Soc. London, A242, 493 (1957).
M. Hindmarsh and A. Rajantie, Phys. Rev. Lett. 84, 1248 (2000)
A. Rajantie, these proceedings.
R. Carmi and E. Polturak, Phys. Rev. B60, 7595 (1999).
N. Martuciello, J. Mygind, V.P. Koshelets, A.V. Shchukin, L.V. Filippenko and R. Monaco, Phys. Rev. B57, 5444 (1998).
R. Monaco, R.J. Rivers and E. Kavoussanaki, these proceedings.
R. Carmi, E. Polturak, and G. Koren, Phys. Rev. Lett. 84, 4996 (2000)
R.J. Rivers, e-print cond-mat/0010346
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Rivers, R.J. Zurek-Kibble Causality Bounds in Time-Dependent Ginzburg-Landau Theory and Quantum Field Theory. Journal of Low Temperature Physics 124, 41–83 (2001). https://doi.org/10.1023/A:1017513531901
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DOI: https://doi.org/10.1023/A:1017513531901