1,810 research outputs found
The Hartree ensemble approximation revisited: The "symmetric phase"
The Hartree ensemble approximation is studied in the ``symmetric phase'' of
1+1 dimensional lambda phi^4 theory. In comparison with the ``broken phase''
studied previously, it is shown that the dynamical evolution of observables
such as the particle distribution, energy exchange and auto-correlation
functions, is substantially slower. Approximate thermalization is found only
for relatively large energy densities and couplings.Comment: 17 pages RevTeX, 16 figures, 3 tables, uses amsmath and feynmp.
Extended some sections, reordered Sec.IV, added 3 refs, numerical typo
corrected, published versio
Exact and Truncated Dynamics in Nonequilibrium Field Theory
Nonperturbative dynamics of quantum fields out of equilibrium is often
described by the time evolution of a hierarchy of correlation functions, using
approximation methods such as Hartree, large N, and nPI-effective action
techniques. These truncation schemes can be implemented equally well in a
classical statistical system, where results can be tested by comparison with
the complete nonlinear evolution obtained by numerical methods. For a 1+1
dimensional scalar field we find that the early-time behaviour is reproduced
qualitatively by the Hartree dynamics. The inclusion of direct scattering
improves this to the quantitative level. We show that the emergence of
nonthermal temperature profiles at intermediate times can be understood in
terms of the fixed points of the evolution equations in the Hartree
approximation. The form of the profile depends explicitly on the initial
ensemble. While the truncated evolution equations do not seem to be able to get
away from the fixed point, the full nonlinear evolution shows thermalization
with a (surprisingly) slow relaxation.Comment: 30 pages with 12 eps figures, minor changes; to appear in Phys.Rev.
Looking for defects in the 2PI correlator
Truncations of the 2PI effective action are seen as a promising way of
studying non-equilibrium dynamics in quantum field theories. We probe their
applicability in the non-perturbative setting of topological defect formation
in a symmetry-breaking phase transition, by comparing full classical lattice
field simulations and the 2PI formulation for classical fields in an O()
symmetric scalar field theory. At next-to-leading order in 1/N, the 2PI
formalism fails to reproduce any signals of defects in the two-point function.
This suggests that one should be careful when applying the 2PI formalism for
symmetry breaking phase transitions.Comment: 22 pages, 6 figure
Dynamics of broken symmetry lambda phi^4 field theory
We study the domain of validity of a Schwinger-Dyson (SD) approach to
non-equilibrium dynamics when there is broken symmetry. We perform exact
numerical simulations of the one- and two-point functions of lambda phi^4 field
theory in 1+1 dimensions in the classical domain for initial conditions where <
phi(x) > not equal to 0. We compare these results to two self-consistent
truncations of the SD equations which ignore three-point vertex function
corrections. The first approximation, which sets the three-point function to
one (the bare vertex approximation (BVA)) gives an excellent description for <
phi(x) > = phi(t). The second approximation which ignores higher in 1/N
corrections to the 2-PI generating functional (2PI -1/N expansion) is not as
accurate for phi(t). Both approximations have serious deficiencies in
describing the two-point function when phi(0) > .4.Comment: 10 pages, 6 figure
Transport coefficients from the 2PI effective action
We show that the lowest nontrivial truncation of the two-particle irreducible
(2PI) effective action correctly determines transport coefficients in a weak
coupling or 1/N expansion at leading (logarithmic) order in several
relativistic field theories. In particular, we consider a single real scalar
field with cubic and quartic interactions in the loop expansion, the O(N) model
in the 2PI-1/N expansion, and QED with a single and many fermion fields.
Therefore, these truncations will provide a correct description, to leading
(logarithmic) order, of the long time behavior of these systems, i.e. the
approach to equilibrium. This supports the promising results obtained for the
dynamics of quantum fields out of equilibrium using 2PI effective action
techniques.Comment: 5 pages, explanation in introduction expanded, summary added; to
appear in PR
The approach to thermalization in the classical phi^4 theory in 1+1 dimensions: energy cascades and universal scaling
We study the dynamics of thermalization and the approach to equilibrium in
the classical phi^4 theory in 1+1 spacetime dimensions. At thermal equilibrium
we exploit the equivalence between the classical canonical averages and
transfer matrix quantum traces of the anharmonic oscillator to obtain exact
results for the temperature dependence of several observables, which provide a
set of criteria for thermalization. We find that the Hartree approximation is
remarkably accurate in equilibrium. The non-equilibrium dynamics is studied by
numerically solving the equations of motion in light-cone coordinates for a
broad range of initial conditions and energy densities.The time evolution is
described by several stages with a cascade of energy towards the ultraviolet.
After a transient stage, the spatio-temporal gradient terms become larger than
the nonlinear term and a stage of universal cascade emerges.This cascade starts
at a time scale t_0 independent of the initial conditions (except for very low
energy density). Here the power spectra feature universal scaling behavior and
the front of the cascade k(t) grows as a power law k(t) sim t^alpha with alpha
lesssim 0.25. The wake behind the cascade is described as a state of Local
Thermodynamic Equilibrium (LTE) with all correlations being determined by the
equilibrium functional form with an effective time dependent temperatureTeff(t)
which slowly decreases as sim t^{-alpha}.Two well separated time scales emerge
while Teff(t) varies slowly, the wavectors in the wake with k < k(t) attain LTE
on much shorter time scales.This universal scaling stage ends when the front of
the cascade reaches the cutoff at a time t_1 sim a^{-1/alpha}. Virialization
starts to set much earlier than LTE. We find that strict thermalization is
achieved only for an infinite time scale.Comment: relevance for quantum field theory discussed providing validity
criteria. To appear in Phys. Rev.
Complex Langevin: Etiology and Diagnostics of its Main Problem
The complex Langevin method is a leading candidate for solving the so-called
sign problem occurring in various physical situations. Its most vexing problem
is that in some cases it produces `convergence to the wrong limit'. In the
first part of the paper we go through the formal justification of the method,
identify points at which it may fail and identify a necessary and sufficient
criterion for correctness. This criterion would, however, require checking
infinitely many identities, and therefore is somewhat academic. We propose
instead a truncation to the check of a few identities; this still gives a
necessary criterion, but a priori it is not clear whether it remains
sufficient. In the second part we carry out a detailed study of two toy models:
first we identify the reasons why in some cases the method fails, second we
test the efficiency of the truncated criterion and find that it works perfectly
at least in the toy models studied.Comment: 39 pages, 15 figures; typos corrected and reference adde
Out-of-equilibrium quantum fields with conserved charge
We study the out-of-equilibrium evolution of an O(2)-invariant scalar field
in which a conserved charge is stored. We apply a loop expansion of the
2-particle irreducible effective action to 3-loop order. Equations of motion
are derived which conserve both total charge and total energy yet allow for the
effects of scattering whereby charge and energy can transfer between modes.
Working in (1+1)-dimensions we solve the equations of motion numerically for a
system knocked out of equilibrium by a sudden temperature quench. We examine
the initial stages of the charge and energy redistribution. This provides a
basis from which we can understand the formation of Bose-Einstein condensates
from first principles.Comment: 11 pages, 5 figures, replacement with improved presentatio
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