1,031 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
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.
Dissipation in equations of motion of scalar fields
The methods of non-equilibrium quantum field theory are used to investigate
the possibility of representing dissipation in the equation of motion for the
expectation value of a scalar field by a friction term, such as is commonly
included in phenomenological inflaton equations of motion. A sequence of
approximations is exhibited which reduces the non-equilibrium theory to a set
of local evolution equations. However, the adiabatic solution to these
evolution equations which is needed to obtain a local equation of motion for
the expectation value is not well defined; nor, therefore, is the friction
coefficient. Thus, a non-equilibrium treatment is essential, even for a system
that remains close to thermal equilibrium, and the formalism developed here
provides one means of achieving this numerically.Comment: 17 pages, 5 figure
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.
Numerical investigation of friction in inflaton equations of motion
The equation of motion for the expectation value of a scalar quantum field
does not have the local form that is commonly assumed in studies of
inflationary cosmology. We have recently argued that the true, temporally
non-local equation of motion does not possess a time-derivative expansion and
that the conversion of inflaton energy into particles is not, in principle,
described by the friction term estimated from linear response theory. Here, we
use numerical methods to investigate whether this obstacle to deriving a local
equation of motion is purely formal, or of some quantitative importance. Using
a simple scalar-field model, we find that, although the non-equilibrium
evolution can exhibit significant damping, this damping is not well described
by the local equation of motion obtained from linear response theory. It is
possible that linear response theory does not apply to the situation we study
only because thermalization turns out to be slow, but we argue that that the
large discrepancies we observe indicate a failure of the local approximation at
a more fundamental level.Comment: 13 pages, 7 figure
Treatment options for recurrent glioblastoma: a network meta-analysis
This is a protocol for a Cochrane Review (Intervention). The objectives are as follows:. To evaluate the effectiveness of further treatment/s for first and subsequent recurrence of glioblastoma multiforme (GBM) among people who have received the standard of care for primary treatment of the disease (chemoradiotherapy) or following development of GBM from a lower grade (radiotherapy with subsequent temozolomide at relapse); and to prepare a brief economic commentary on the available evidence
An Analytic Equation of State for Ising-like Models
Using an Environmentally Friendly Renormalization we derive, from an
underlying field theory representation, a formal expression for the equation of
state, , that exhibits all desired asymptotic and analyticity
properties in the three limits , and . The only
necessary inputs are the Wilson functions , and
, associated with a renormalization of the transverse vertex
functions. These Wilson functions exhibit a crossover between the Wilson-Fisher
fixed point and the fixed point that controls the coexistence curve.
Restricting to the case N=1, we derive a one-loop equation of state for naturally parameterized by a ratio of non-linear scaling fields. For
we show that a non-parameterized analytic form can be deduced. Various
asymptotic amplitudes are calculated directly from the equation of state in all
three asymptotic limits of interest and comparison made with known results. By
positing a scaling form for the equation of state inspired by the one-loop
result, but adjusted to fit the known values of the critical exponents, we
obtain better agreement with known asymptotic amplitudes.Comment: 10 pages, 2 figure
Critical temperature for first-order phase transitions in confined systems
We consider the Euclidean -dimensional
() model with () compactified dimensions.
Introducing temperature by means of the Ginzburg--Landau prescription in the
mass term of the Hamiltonian, this model can be interpreted as describing a
first-order phase transition for a system in a region of the -dimensional
space, limited by pairs of parallel planes, orthogonal to the coordinates
axis . The planes in each pair are separated by distances
. We obtain an expression for the transition temperature as
a function of the size of the system, , . For
D=3 we particularize this formula, taking for the
physically interesting cases (a film), (an infinitely long wire
having a square cross-section), and for (a cube). For completeness, the
corresponding formulas for second-order transitions are also presented.
Comparison with experimental data for superconducting films and wires shows
qualitative agreement with our theoretical expressionsComment: REVTEX, 11 pages, 3 figures; to appear in Eur. Phys. Journal
Scaling in high-temperature superconductors
A Hartree approximation is used to study the interplay of two kinds of
scaling which arise in high-temperature superconductors, namely critical-point
scaling and that due to the confinement of electron pairs to their lowest
Landau level in the presence of an applied magnetic field. In the neighbourhood
of the zero-field critical point, thermodynamic functions scale with the
scaling variable , which differs from the variable
suggested by the gaussian approximation.
Lowest-Landau-level (LLL) scaling occurs in a region of high field surrounding
the upper critical field line but not in the vicinity of the zero-field
transition. For YBaCuO in particular, a field of at least 10 T is needed to
observe LLL scaling. These results are consistent with a range of recent
experimental measurements of the magnetization, transport properties and,
especially, the specific heat of high- materials.Comment: 22 pages + 1 figure appended as postscript fil
Large-N theory of strongly commensurate dirty-bosons: absence of transition in two dimensions
The spherical limit of strongly commensurate dirty-bosons is studied
perturbatively at weak disorder and numerically at strong disorder in two
dimensions (2D). We argue that disorder is not perfectly screened by
interactions, and consequently that the ground state in the effective Anderson
localisation problem always remains localised. As a result there is only a
gapped Mott insulator phase in the theory. Comparisons with other studies and
the parallel with disordered fermions in 2D are discussed. We conjecture that
while for the physical cases N=2 (XY) and N=1 (Ising) the theory should have
the ordered phase, it may not for N=3 (Heisenberg).Comment: 15 pages, 4 figures. Minor typographical errors correcte
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