19 research outputs found
Renormalization group and nonequilibrium action in stochastic field theory
We investigate the renormalization group approach to nonequilibrium field
theory. We show that it is possible to derive nontrivial renormalization group
flow from iterative coarse graining of a closed-time-path action. This
renormalization group is different from the usual in quantum field theory
textbooks, in that it describes nontrivial noise and dissipation. We work out a
specific example where the variation of the closed-time-path action leads to
the so-called Kardar-Parisi-Zhang equation, and show that the renormalization
group obtained by coarse graining this action, agrees with the dynamical
renormalization group derived by directly coarse graining the equations of
motion.Comment: 33 pages, 3 figures included in the text. Revised; one reference
adde
Noise induced transitions in semiclassical cosmology
A semiclassical cosmological model is considered which consists of a closed
Friedmann-Robertson-Walker in the presence of a cosmological constant, which
mimics the effect of an inflaton field, and a massless, non-conformally coupled
quantum scalar field. We show that the back-reaction of the quantum field,
which consists basically of a non local term due to gravitational particle
creation and a noise term induced by the quantum fluctuations of the field, are
able to drive the cosmological scale factor over the barrier of the classical
potential so that if the universe starts near zero scale factor (initial
singularity) it can make the transition to an exponentially expanding de Sitter
phase. We compute the probability of this transition and it turns out to be
comparable with the probability that the universe tunnels from "nothing" into
an inflationary stage in quantum cosmology. This suggests that in the presence
of matter fields the back-reaction on the spacetime should not be neglected in
quantum cosmology.Comment: LaTex, 33.tex pages, no figure
Shear Viscosity in the O(N) Model
We compute the shear viscosity in the O(N) model at first nontrivial order in
the large N expansion. The calculation is organized using the 1/N expansion of
the 2PI effective action (2PI-1/N expansion) to next-to-leading order, which
leads to an integral equation summing ladder and bubble diagrams. We also
consider the weakly coupled theory for arbitrary N, using the three-loop
expansion of the 2PI effective action. In the limit of weak coupling and
vanishing mass, we find an approximate analytical solution of the integral
equation. For general coupling and mass, the integral equation is solved
numerically using a variational approach. The shear viscosity turns out to be
close to the result obtained in the weak-coupling analysis.Comment: 37 pages, few typos corrected; to appear in JHE
Magnetic field generation from non-equilibrium phase transitions
We study the generation of magnetic fields during the stage of particle
production resulting from spinodal instabilities during phase transitions out
of equilibrium. The main premise is that long-wavelength instabilities that
drive the phase transition lead to strong non-equilibrium charge and current
fluctuations which generate electromagnetic fields. We present a formulation
based on the non-equilibrium Schwinger-Dyson equations that leads to an exact
expression for the spectrum of electromagnetic fields valid for general
theories and cosmological backgrounds and whose main ingredient is the
transverse photon polarization out of equilibrium. This formulation includes
the dissipative effects of the conductivity in the medium. As a prelude to
cosmology we study magnetogenesis in Minkowski space-time in a theory of N
charged scalar fields to lowest order in the gauge coupling and to leading
order in the large N within two scenarios of cosmological relevance. The
long-wavelength power spectrum for electric and magnetic fields at the end of
the phase transition is obtained explicitly.
It follows that equipartition between electric and magnetic fields does not
hold out of equilibrium. In the case of a transition from a high temperature
phase, the conductivity of the medium severely hinders the generation of
magnetic fields, however the magnetic fields generated are correlated on scales
of the order of the domain size, which is much larger than the magnetic
diffusion length. Implications of the results to cosmological phase transitions
driven by spinodal unstabilities are discussed.Comment: Preprint no. LPTHE 02-55, 30 pages, latex, 2 eps figures. Added one
reference. To appear in Phys. Rev.
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
Transport coefficients in high temperature gauge theories: (II) Beyond leading log
Results are presented of a full leading-order evaluation of the shear
viscosity, flavor diffusion constants, and electrical conductivity in high
temperature QCD and QED. The presence of Coulomb logarithms associated with
gauge interactions imply that the leading-order results for transport
coefficients may themselves be expanded in an infinite series in powers of
1/log(1/g); the utility of this expansion is also examined. A
next-to-leading-log approximation is found to approximate the full
leading-order result quite well as long as the Debye mass is less than the
temperature.Comment: 38 pages, 6 figure
Decoherence of Histories and Hydrodynamic Equations for a Linear Oscillator Chain
We investigate the decoherence of histories of local densities for linear
oscillators models. It is shown that histories of local number, momentum and
energy density are approximately decoherent, when coarse-grained over
sufficiently large volumes. Decoherence arises directly from the proximity of
these variables to exactly conserved quantities (which are exactly decoherent),
and not from environmentally-induced decoherence. We discuss the approach to
local equilibrium and the subsequent emergence of hydrodynamic equations for
the local densities.Comment: 37 pages, RevTe
Large scale magnetogenesis from a non-equilibrium phase transition in the radiation dominated era
We study the generation of large scale primordial magnetic fields by a
cosmological phase transition during the radiation dominated era. The setting
is a theory of N charged scalar fields coupled to an abelian gauge field, that
undergoes a phase transition at a critical temperature much larger than the
electroweak scale. The dynamics after the transition features two distinct
stages: a spinodal regime dominated by linear long-wavelength instabilities,
and a scaling stage in which the non-linearities and backreaction of the scalar
fields are dominant. This second stage describes the growth of horizon sized
domains. We implement a recently introduced formulation to obtain the spectrum
of magnetic fields that includes the dissipative effects of the plasma. We find
that large scale magnetogenesis is very efficient during the scaling regime.
The ratio between the energy density on scales larger than L and that in the
background radiation r(L,T) = rho_B(L,T)/rho_{cmb}(T) is r(L,T) \sim 10^{-34}
at the Electroweak scale and r(L,T) \sim 10^{-14} at the QCD scale for L \sim 1
Mpc. The resulting spectrum is insensitive to the magnetic diffusion length. We
conjecture that a similar mechanism could be operative after the QCD chiral
phase transition.Comment: LaTex, 25 pages, no figures, to appear in Phys. Rev.
Schwinger-Dyson approach to non-equilibrium classical field theory
In this paper we discuss a Schwinger-Dyson [SD] approach for determining the
time evolution of the unequal time correlation functions of a non-equilibrium
classical field theory, where the classical system is described by an initial
density matrix at time . We focus on field theory in 1+1
space time dimensions where we can perform exact numerical simulations by
sampling an ensemble of initial conditions specified by the initial density
matrix. We discuss two approaches. The first, the bare vertex approximation
[BVA], is based on ignoring vertex corrections to the SD equations in the
auxiliary field formalism relevant for 1/N expansions. The second approximation
is a related approximation made to the SD equations of the original formulation
in terms of alone. We compare these SD approximations as well as a
Hartree approximation with exact numerical simulations. We find that both
approximations based on the SD equations yield good agreement with exact
numerical simulations and cure the late time oscillation problem of the Hartree
approximation. We also discuss the relationship between the quantum and
classical SD equations.Comment: 36 pages, 5 figure
A Step Beyond the Bounce: Bubble Dynamics in Quantum Phase Transitions
We study the dynamical evolution of a phase interface or bubble in the
context of a \lambda \phi^4 + g \phi^6 scalar quantum field theory. We use a
self-consistent mean-field approximation derived from a 2PI effective action to
construct an initial value problem for the expectation value of the quantum
field and two-point function. We solve the equations of motion numerically in
(1+1)-dimensions and compare the results to the purely classical evolution. We
find that the quantum fluctuations dress the classical profile, affecting both
the early time expansion of the bubble and the behavior upon collision with a
neighboring interface.Comment: 12 pages, multiple figure