2,401 research outputs found
Perturbative nonequilibrium dynamics of phase transitions in an expanding universe
A complete set of Feynman rules is derived, which permits a perturbative
description of the nonequilibrium dynamics of a symmetry-breaking phase
transition in theory in an expanding universe. In contrast to a
naive expansion in powers of the coupling constant, this approximation scheme
provides for (a) a description of the nonequilibrium state in terms of its own
finite-width quasiparticle excitations, thus correctly incorporating
dissipative effects in low-order calculations, and (b) the emergence from a
symmetric initial state of a final state exhibiting the properties of
spontaneous symmetry breaking, while maintaining the constraint . Earlier work on dissipative perturbation theory and spontaneous symmetry
breaking in Minkowski spacetime is reviewed. The central problem addressed is
the construction of a perturbative approximation scheme which treats the
initial symmetric state in terms of the field , while the state that
emerges at later times is treated in terms of a field , linearly related
to . The connection between early and late times involves an infinite
sequence of composite propagators. Explicit one-loop calculations are given of
the gap equations that determine quasiparticle masses and of the equation of
motion for and the renormalization of these equations is
described. The perturbation series needed to describe the symmetric and
broken-symmetry states are not equivalent, and this leads to ambiguities
intrinsic to any perturbative approach. These ambiguities are discussed in
detail and a systematic procedure for matching the two approximations is
described.Comment: 22 pages, using RevTeX. 6 figures. Submitted to Physical Review
Crossover from the pair contact process with diffusion to directed percolation
Crossover behaviors from the pair contact process with diffusion (PCPD) and
the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one
dimension by introducing a single particle annihilation/branching dynamics. The
crossover exponents are estimated numerically as for the PCPD and for the DPCPD.
Nontriviality of the PCPD crossover exponent strongly supports non-DP nature of
the PCPD critical scaling, which is further evidenced by the anomalous critical
amplitude scaling near the PCPD point. In addition, we find that the DPCPD
crossover is consistent with the mean field prediction of the tricritical DP
class as expected
Nonequilibrium perturbation theory for complex scalar fields
Real-time perturbation theory is formulated for complex scalar fields away
from thermal equilibrium in such a way that dissipative effects arising from
the absorptive parts of loop diagrams are approximately resummed into the
unperturbed propagators. Low order calculations of physical quantities then
involve quasiparticle occupation numbers which evolve with the changing state
of the field system, in contrast to standard perturbation theory, where these
occupation numbers are frozen at their initial values. The evolution equation
of the occupation numbers can be cast approximately in the form of a Boltzmann
equation. Particular attention is given to the effects of a non-zero chemical
potential, and it is found that the thermal masses and decay widths of
quasiparticle modes are different for particles and antiparticles.Comment: 15 pages using RevTeX; 2 figures in 1 Postscript file; Submitted to
Phys. Rev.
Comments on a class of orthogonality relations relevant to fluid-structure interaction
Copyright @ 2011 Springer Science+Business Media B.V
Crossover from the parity-conserving pair contact process with diffusion to other universality classes
The pair contact process with diffusion (PCPD) with modulo 2 conservation
(\pcpdt) [, ] is studied in one dimension, focused on the
crossover to other well established universality classes: the directed Ising
(DI) and the directed percolation (DP). First, we show that the \pcpdt shares
the critical behaviors with the PCPD, both with and without directional bias.
Second, the crossover from the \pcpdt to the DI is studied by including a
parity-conserving single-particle process (). We find the crossover
exponent , which is argued to be identical to that of the
PCPD-to-DP crossover by adding . This suggests that the PCPD
universality class has a well defined fixed point distinct from the DP. Third,
we study the crossover from a hybrid-type reaction-diffusion process belonging
to the DP [, ] to the DI by adding . We find
for the DP-to-DI crossover. The inequality of and
further supports the non-DP nature of the PCPD scaling. Finally, we
introduce a symmetry-breaking field in the dual spin language to study the
crossover from the \pcpdt to the DP. We find , which is
associated with a new independent route from the PCPD to the DP.Comment: 8 pages, 8 figure
Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states
At non-equilibrium phase transitions into absorbing (trapped) states, it is
well known that the directed percolation (DP) critical scaling is shared by two
classes of models with a single (S) absorbing state and with infinitely many
(IM) absorbing states. We study the crossover behavior in one dimension,
arising from a considerable reduction of the number of absorbing states
(typically from the IM-type to the S-type DP models), by following two
different (excitatory or inhibitory) routes which make the auxiliary field
density abruptly jump at the crossover. Along the excitatory route, the system
becomes overly activated even for an infinitesimal perturbation and its
crossover becomes discontinuous. Along the inhibitory route, we find continuous
crossover with the universal crossover exponent , which is
argued to be equal to , the relaxation time exponent of the DP
universality class on a general footing. This conjecture is also confirmed in
the case of the directed Ising (parity-conserving) class. Finally, we discuss
the effect of diffusion to the IM-type models and suggest an argument why
diffusive models with some hybrid-type reactions should belong to the DP class.Comment: 8 pages, 9 figure
Friction in inflaton equations of motion
The possibility of a friction term in the equation of motion for a scalar
field is investigated in non-equilibrium field theory. The results obtained
differ greatly from existing estimates based on linear response theory, and
suggest that dissipation is not well represented by a term of the form
.Comment: 4 pages, 2 figures, RevTex4. An obscurity in the original version has
been clarifie
Nonequilibrium perturbation theory for spin-1/2 fields
A partial resummation of perturbation theory is described for field theories
containing spin-1/2 particles in states that may be far from thermal
equilibrium. This allows the nonequilibrium state to be characterized in terms
of quasiparticles that approximate its true elementary excitations. In
particular, the quasiparticles have dispersion relations that differ from those
of free particles, finite thermal widths and occupation numbers which, in
contrast to those of standard perturbation theory evolve with the changing
nonequilibrium environment. A description of this kind is essential for
estimating the evolution of the system over extended periods of time. In
contrast to the corresponding description of scalar particles, the structure of
nonequilibrium fermion propagators exhibits features which have no counterpart
in the equilibrium theory.Comment: 16 pages; no figures; submitted to Phys. Rev.
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