Nonequilibrium evolution in scalar O(n) models with spontaneous symmetry breaking

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a scalar O(N) model with spontaneously broken symmetry. In contrast to previous studies we do not consider the large N limit, but the case of finite N, including N=1, i.e., plain

\lambda \phi^ 4

theory. The instabilities encountered in the one-loop approximation are prevented, as in the large-N limit, by back reaction of the fluctuations on themselves, or, equivalently, by including a resummation of bubble diagrams. For this resummation and its renormalization we use formulations developed recently based on the effective action formalism of Cornwall, Jackiw and Tomboulis. The formulation of renormalized equations for finite N derived here represents a useful tool for simulations with realistic models. Here we concentrate on the phase structure of such models. We observe the transition between the spontaneously broken and the symmetric phase at low and high energy densities, respectively. This shows that the typical structures expected in thermal equilibrium are encountered in nonequilibrium dynamics even at early times, i.e., before an efficient rescattering can lead to thermalization.

Note:

31 pages, 19 Figures, LaTeX; extended discussion on the basis of: fluctuations, eff. potential, correlations, analytic calculation of parametric resonance for "pion"_and_ "sigma" fields

05.70.Fh
11.15.Pg
03.65.Sq
11.30.Qc
field theory: scalar
symmetry: O(N)
spontaneous symmetry breaking
condensation
critical phenomena
renormalization

References(57)

Figures(0)

Spontaneous Symmetry Breaking in the O(N) Model for Large N*

- Phys.Rev.D 10 (1974) 2491
•
DOI:
- 10.1103/PhysRevD.10.2491

Symmetry Behavior at Finite Temperature

L. Dolan
(
- MIT, LNS
)
,
R. Jackiw
(
- MIT, LNS
)

- Phys.Rev.D 9 (1974) 3320-3341
•
DOI:
- 10.1103/PhysRevD.9.3320

Phase Structure of the O(N) Vector Model

William A. Bardeen
(
- Fermilab
)
,
Moshe Moshe
(
- Fermilab
)

- Phys.Rev.D 28 (1983) 1372
•
DOI:
- 10.1103/PhysRevD.28.1372

Comment on the Finite Temperature Behavior of $\Lambda (\phi^2$ )**2 in Four-dimensions Theory

William A. Bardeen
(
- Munich, Max Planck Inst. and
- Technion
)
,
M. Moshe
(
- Munich, Max Planck Inst. and
- Technion
)

- Phys.Rev.D 34 (1986) 1229-1231
•
DOI:
- 10.1103/PhysRevD.34.1229

Closed Time Path Functional Formalism in Curved Space-Time: Application to Cosmological Back Reaction Problems

E. Calzetta
(
- Maryland U.
)
,
B.L. Hu
(
- Maryland U.
)

- Phys.Rev.D 35 (1987) 495
•
DOI:
- 10.1103/PhysRevD.35.495

Nonequilibrium Quantum Fields: Closed Time Path Effective Action, Wigner Function and Boltzmann Equation

E. Calzetta
(
- Maryland U.
)
,
B.L. Hu
(
- Maryland U.
)

- Phys.Rev.D 37 (1988) 2878
•
DOI:
- 10.1103/PhysRevD.37.2878

Nonequilibrium quantum fields in the large N expansion

et al.

- Phys.Rev.D 50 (1994) 2848-2869
•
e-Print:
- hep-ph/9405352
•
DOI:
- 10.1103/PhysRevD.50.2848

Nonequilibrium evolution of scalar fields in FRW cosmologies I

- Phys.Rev.D 49 (1994) 2769-2785
•
e-Print:
- hep-ph/9310319
•
DOI:
- 10.1103/PhysRevD.49.2769

Dissipation via particle production in scalar field theories

- Phys.Rev.D 51 (1995) 4419-4444
•
e-Print:
- hep-ph/9408214
•
DOI:
- 10.1103/PhysRevD.51.4419

Reheating and thermalization: Linear versus nonlinear relaxation

D. Boyanovsky
(
- Pittsburgh U.
)
,
M. D'Attanasio
(
- Paris U., VI-VII and
- INFN, Parma
)
,
H.J. de Vega
(
- Paris U., VI-VII
)
,
R. Holman
(
- Carnegie Mellon U.
)
,
D.-S. Lee
(
- Pittsburgh U.
)

- Phys.Rev.D 52 (1995) 6805-6827
•
e-Print:
- hep-ph/9507414
•
DOI:
- 10.1103/PhysRevD.52.6805

Nonequilibrium dynamics: A Renormalized computation scheme

- Phys.Rev.D 55 (1997) 2320-2330
•
e-Print:
- hep-th/9608006
•
DOI:
- 10.1103/PhysRevD.55.2320

Nonequilibrium dynamics of symmetry breaking in lambda Phi**4 field theory

- Phys.Rev.D 55 (1997) 6471-6503
•
e-Print:
- hep-ph/9610345
•
DOI:
- 10.1103/PhysRevD.55.6471

Analytic and numerical study of preheating dynamics

- Phys.Rev.D 54 (1996) 7570-7598
•
e-Print:
- hep-ph/9608205
•
DOI:
- 10.1103/PhysRevD.54.7570

Asymptotic dynamics in scalar field theory: Anomalous relaxation

D. Boyanovsky
(
- Pittsburgh U.
)
,
C. Destri
(
- Milan U. and
- INFN, Milan
)
,
H.J. de Vega
(
- Paris U., VI-VII
)
,
R. Holman
(
- Carnegie Mellon U.
)
,
J. Salgado
(
- Paris U., VI-VII
)

- Phys.Rev.D 57 (1998) 7388-7415
•
e-Print:
- hep-ph/9711384
•
DOI:
- 10.1103/PhysRevD.57.7388

Nonequilibrium Bose-Einstein condensates, dynamical scaling and symmetric evolution in the large N Phi**4 theory

- Phys.Rev.D 59 (1999) 125009
•
e-Print:
- hep-ph/9811273
•
DOI:
- 10.1103/PhysRevD.59.125009

Nonequilibrium evolution and symmetry structure of the large N Phi**4 model at finite temperature

Jurgen Baacke
(
- Dortmund U.
)
,
Katrin Heitmann
(
- Dortmund U.
)

- Phys.Rev.D 62 (2000) 105022
•
e-Print:
- hep-ph/0003317
•
DOI:
- 10.1103/PhysRevD.62.105022

- J.Phys. AG26 431

Out-of-equilibrium dynamics of large N phi**4 QFT in finite volume

C. Destri
(
- Milan Bicocca U. and
- INFN, Milan and
- Milan U.
)
,
E. Manfredini
(
- Milan U. and
- INFN, Milan
)

- Phys.Rev.D 62 (2000) 025007
•
e-Print:
- hep-ph/0001177
•
DOI:
- 10.1103/PhysRevD.62.025007

An Improved time dependent Hartree-Fock approach for scalar phi**4 QFT

C. Destri
(
- Milan Bicocca U. and
- INFN, Milan and
- Milan U.
)
,
E. Manfredini
(
- Milan U. and
- INFN, Milan
)

- Phys.Rev.D 62 (2000) 025008
•
e-Print:
- hep-ph/0001178
•
DOI:
- 10.1103/PhysRevD.62.025008

Selfconsistent improvement of the finite temperature effective potential

G. Amelino-Camelia
(
- Boston U.
)
,
So-Young Pi
(
- Boston U.
)

- Phys.Rev.D 47 (1993) 2356-2362
•
e-Print:
- hep-ph/9211211
•
DOI:
- 10.1103/PhysRevD.47.2356

Thermal effective potential of the O(N) linear sigma model

Giovanni Amelino-Camelia
(
- Oxford U.
)

- Phys.Lett.B 407 (1997) 268-274
•
e-Print:
- hep-ph/9702403
•
DOI:
- 10.1016/S0370-2693(97)00709-0

Soft modes associated with chiral transition at finite temperature

S. Chiku
(
- Tsukuba U.
)
,
T. Hatsuda
(
- Tsukuba U.
)

- Phys.Rev.D 57 (1998) 6-9
•
e-Print:
- hep-ph/9706453
•
DOI:
- 10.1103/PhysRevD.57.R6

Optimized perturbation theory at finite temperature

S. Chiku
(
- Tsukuba U.
)
,
T. Hatsuda
(
- Tsukuba U.
)

- Phys.Rev.D 58 (1998) 076001
•
e-Print:
- hep-ph/9803226
•
DOI:
- 10.1103/PhysRevD.58.076001

Effective Action for Composite Operators

- Phys.Rev.D 10 (1974) 2428-2445,
- Also in *Farhi, E. (ed.), Jackiw, R. (ed.): Dynamical Gauge Symmetry Breaking*, 108-125
•
DOI:
- 10.1103/PhysRevD.10.2428

Effective potential of O(N) linear sigma model at finite temperature

Y. Nemoto
(
- Tokyo Inst. Tech. and
- Osaka U., Res. Ctr. Nucl. Phys.
)
,
K. Naito
(
- Tokyo Inst. Tech. and
- Wako, RIKEN
)
,
M. Oka
(
- Tokyo Inst. Tech.
)

- Eur.Phys.J.A 9 (2000) 245-259
•
e-Print:
- hep-ph/9911431
•
DOI:
- 10.1007/s100500070042

1-25 of 57
1
2
3
25 / page