111 research outputs found
Mode decomposition and renormalization in semiclassical gravity
We compute the influence action for a system perturbatively coupled to a
linear scalar field acting as the environment. Subtleties related to
divergences that appear when summing over all the modes are made explicit and
clarified. Being closely connected with models used in the literature, we show
how to completely reconcile the results obtained in the context of stochastic
semiclassical gravity when using mode decomposition with those obtained by
other standard functional techniques.Comment: 4 pages, RevTeX, no figure
Semiclassical Effects and the Onset of Inflation
We present a class of exact solutions to the constraint equations of General
Relativity coupled to a Klein - Gordon field, these solutions being isotropic
but not homogeneous. We analyze the subsequent evolution of the consistent
Cauchy data represented by those solutions, showing that only certain special
initial conditions eventually lead to successfull Inflationary cosmologies. We
argue, however, that these initial conditions are precisely the likely outcomes
of quantum events occurred before the inflationary era.Comment: 22 pages, file written in RevTe
Fluctuations of the vacuum energy density of quantum fields in curved spacetime via generalized zeta functions
For quantum fields on a curved spacetime with an Euclidean section, we derive
a general expression for the stress energy tensor two-point function in terms
of the effective action. The renormalized two-point function is given in terms
of the second variation of the Mellin transform of the trace of the heat kernel
for the quantum fields. For systems for which a spectral decomposition of the
wave opearator is possible, we give an exact expression for this two-point
function. Explicit examples of the variance to the mean ratio of the vacuum energy density of a
massless scalar field are computed for the spatial topologies of and , with results of , and
respectively. The large variance signifies the importance
of quantum fluctuations and has important implications for the validity of
semiclassical gravity theories at sub-Planckian scales. The method presented
here can facilitate the calculation of stress-energy fluctuations for quantum
fields useful for the analysis of fluctuation effects and critical phenomena in
problems ranging from atom optics and mesoscopic physics to early universe and
black hole physics.Comment: Uses revte
Noise and Fluctuations in Semiclassical Gravity
We continue our earlier investigation of the backreaction problem in
semiclassical gravity with the Schwinger-Keldysh or closed-time-path (CTP)
functional formalism using the language of the decoherent history formulation
of quantum mechanics. Making use of its intimate relation with the
Feynman-Vernon influence functional (IF) method, we examine the statistical
mechanical meaning and show the interrelation of the many quantum processes
involved in the backreaction problem, such as particle creation, decoherence
and dissipation. We show how noise and fluctuation arise naturally from the CTP
formalism. We derive an expression for the CTP effective action in terms of the
Bogolubov coefficients and show how noise is related to the fluctuations in the
number of particles created. In so doing we have extended the old framework of
semiclassical gravity, based on the mean field theory of Einstein equation with
a source given by the expectation value of the energy-momentum tensor, to that
based on a Langevin-type equation, where the dynamics of fluctuations of
spacetime is driven by the quantum fluctuations of the matter field. This
generalized framework is useful for the investigation of quantum processes in
the early universe involving fluctuations, vacuum stability and phase transtion
phenomena and the non-equilibrium thermodynamics of black holes. It is also
essential to an understanding of the transition from any quantum theory of
gravity to classical general relativity. \pacs{pacs numbers:
04.60.+n,98.80.Cq,05.40.+j,03.65.Sq}Comment: Latex 37 pages, umdpp 93-216 (submitted to Phys. Rev. D, 24 Nov.
1993
Stochastic Behavior of Effective Field Theories Across Threshold
We explore how the existence of a field with a heavy mass influences the low
energy dynamics of a quantum field with a light mass by expounding the
stochastic characters of their interactions which take on the form of
fluctuations in the number of (heavy field) particles created at the threshold,
and dissipation in the dynamics of the light fields, arising from the
backreaction of produced heavy particles. We claim that the stochastic nature
of effective field theories is intrinsic, in that dissipation and fluctuations
are present both above and below the threshold. Stochasticity builds up
exponentially quickly as the heavy threshold is approached from below, becoming
dominant once the threshold is crossed. But it also exists below the threshold
and is in principle detectable, albeit strongly suppressed at low energies. The
results derived here can be used to give a quantitative definition of the
`effectiveness' of a theory in terms of the relative weight of the
deterministic versus the stochastic behavior at different energy scales.Comment: 32 pages, Latex, no figure
Stochastic semiclassical cosmological models
We consider the classical stochastic fluctuations of spacetime geometry
induced by quantum fluctuations of massless non-conformal matter fields in the
Early Universe. To this end, we supplement the stress-energy tensor of these
fields with a stochastic part, which is computed along the lines of the
Feynman-Vernon and Schwinger-Keldysh techniques; the Einstein equation is
therefore upgraded to a so called Einstein-Langevin equation. We consider in
some detail the conformal fluctuations of flat spacetime and the fluctuations
of the scale factor in a simple cosmological modelintroduced by Hartle, which
consists of a spatially flat isotropic cosmology driven by radiation and dust.Comment: 29 pages, no figures, ReVTeX fil
Macroscopic Quantum Phenomena from the Correlation, Coupling and Criticality Perspectives
In this sequel paper we explore how macroscopic quantum phenomena can be
measured or understood from the behavior of quantum correlations which exist in
a quantum system of many particles or components and how the interaction
strengths change with energy or scale, under ordinary situations and when the
system is near its critical point. We use the nPI (master) effective action
related to the Boltzmann-BBGKY / Schwinger-Dyson hierarchy of equations as a
tool for systemizing the contributions of higher order correlation functions to
the dynamics of lower order correlation functions. Together with the large N
expansion discussed in our first paper(MQP1) we explore 1) the conditions
whereby an H-theorem is obtained, which can be viewed as a signifier of the
emergence of macroscopic behavior in the system. We give two more examples from
past work: 2) the nonequilibrium dynamics of N atoms in an optical lattice
under the large (field components), 2PI and second order perturbative
expansions, illustrating how N and enter in these three aspects of
quantum correlations, coherence and coupling strength. 3) the behavior of an
interacting quantum system near its critical point, the effects of quantum and
thermal fluctuations and the conditions under which the system manifests
infrared dimensional reduction. We also discuss how the effective field theory
concept bears on macroscopic quantum phenomena: the running of the coupling
parameters with energy or scale imparts a dynamical-dependent and an
interaction-sensitive definition of `macroscopia'.Comment: For IARD 2010 meeting, Hualien, Taiwan. Proceedings to appear in J.
Physics (Conf. Series
O(N) Quantum fields in curved spacetime
For the O(N) field theory with lambda Phi^4 self-coupling, we construct the
two-particle-irreducible (2PI), closed-time-path (CTP) effective action in a
general curved spacetime. From this we derive a set of coupled equations for
the mean field and the variance. They are useful for studying the
nonperturbative, nonequilibrium dynamics of a quantum field when full back
reactions of the quantum field on the curved spacetime, as well as the
fluctuations on the mean field, are required. Applications to phase transitions
in the early Universe such as the Planck scale or in the reheating phase of
chaotic inflation are under investigation.Comment: 31 pages, 2 figures, uses RevTeX 3.1, LaTeX 2e, AMSfonts 2.2,
graphics 0.6; To appear in Phys. Rev. D (7/15/97
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