55 research outputs found
Entropy and Uncertainty of Squeezed Quantum Open Systems
We define the entropy S and uncertainty function of a squeezed system interacting with a thermal bath, and study how they change in time by following the evolution of the reduced density matrix in the influence functional formalism. As examples, we calculate the entropy of two exactly solvable squeezed systems: an inverted harmonic oscillator and a scalar field mode evolving in an inflationary universe. For the inverted oscillator with weak coupling to the bath, at both high and low temperatures, , where r is the squeeze parameter. In the de Sitter case, at high temperatures, where , being the coupling to the bath and H the Hubble constant. These three cases confirm previous results based on more ad hoc prescriptions for calculating entropy. But at low temperatures, the de Sitter entropy is noticeably different. This result obtained from a more rigorous approach, shows that factors usually ignored by the conventional approaches, i.e., the nature of the environment and the coupling strength betwen the system and the environment, are important
Entropy and Uncertainty of Squeezed Quantum Open Systems
We define the entropy S and uncertainty function of a squeezed system
interacting with a thermal bath, and study how they change in time by following
the evolution of the reduced density matrix in the influence functional
formalism. As examples, we calculate the entropy of two exactly solvable
squeezed systems: an inverted harmonic oscillator and a scalar field mode
evolving in an inflationary universe. For the inverted oscillator with weak
coupling to the bath, at both high and low temperatures, , where r is
the squeeze parameter. In the de Sitter case, at high temperatures, where , being the coupling to the bath and H
the Hubble constant. These three cases confirm previous results based on more
ad hoc prescriptions for calculating entropy. But at low temperatures, the de
Sitter entropy is noticeably different. This result, obtained
from a more rigorous approach, shows that factors usually ignored by the
conventional approaches, i.e., the nature of the environment and the coupling
strength betwen the system and the environment, are important.Comment: 36 pages, epsfig, 2 in-text figures include
Acoustic Signatures in the Primary Microwave Background Bispectrum
If the primordial fluctuations are non-Gaussian, then this non-Gaussianity
will be apparent in the cosmic microwave background (CMB) sky. With their
sensitive all-sky observation, MAP and Planck satellites should be able to
detect weak non-Gaussianity in the CMB sky. On large angular scale, there is a
simple relationship between the CMB temperature and the primordial curvature
perturbation. On smaller scales; however, the radiation transfer function
becomes more complex. In this paper, we present the angular bispectrum of the
primary CMB anisotropy that uses the full transfer function. We find that the
bispectrum has a series of acoustic peaks that change a sign, and a period of
acoustic oscillations is twice as long as that of the angular power spectrum.
Using a single non-linear coupling parameter to characterize the amplitude of
the bispectrum, we estimate the expected signal-to-noise ratio for COBE, MAP,
and Planck experiments. We find that the detection of the primary bispectrum by
any kind of experiments should be problematic for the simple slow-roll
inflationary scenarios. We compare the sensitivity of the primary bispectrum to
the primary skewness and conclude that when we can compute the predicted form
of the bispectrum, it becomes a ``matched filter'' for detecting the
non-Gaussianity in the data, and much more powerful tool than the skewness. We
also show that MAP and Planck can separate the primary bispectrum from various
secondary bispectra on the basis of the shape difference. The primary CMB
bispectrum is a test of the inflationary scenario, and also a probe of the
non-linear physics in the very early universe.Comment: Submitted to Physical Review D. (v1) letter version [4 pages, 3
figures]. (v2) full paper version including the primary skewness, secondary
bispectra, and the foreground separation [17 pages, 5 figures
Stochastic approach to inflation II: classicality, coarse-graining and noises
In this work we generalize a previously developed semiclassical approach to
inflation, devoted to the analysis of the effective dynamics of coarse-grained
fields, which are essential to the stochastic approach to inflation. We
consider general non-trivial momentum distributions when defining these fields.
The use of smooth cutoffs in momentum space avoids highly singular quantum
noise correlations and allows us to consider the whole quantum noise sector
when analyzing the conditions for the validity of an effective classical
dynamical description of the coarse-grained field. We show that the weighting
of modes has physical consequences, and thus cannot be considered as a mere
mathematical artifact. In particular we discuss the exponential inflationary
scenario and show that colored noises appear with cutoff dependent amplitudes.Comment: 18 pages, revtex, no figure
The Coherent State Representation of Quantum Fluctuations in the Early Universe
Using the squeezed state formalism the coherent state representation of
quantum fluctuations in an expanding universe is derived. It is shown that this
provides a useful alternative to the Wigner function as a phase space
representation of quantum fluctuations. The quantum to classical transition of
fluctuations is naturally implemented by decohering the density matrix in this
representation. The entropy of the decohered vacua is derived. It is shown that
the decoherence process breaks the physical equivalence between vacua that
differ by a coordinate dependent phase generated by a surface term in the
Lagrangian. In particular, scale invariant power spectra are only obtained for
a special choice of surface term.Comment: 25 pages in revtex 3. This version is completely revised with
corrections and significant new calculation
Quantum Vacuum Instability Near Rotating Stars
We discuss the Starobinskii-Unruh process for the Kerr black hole. We show
how this effect is related to the theory of squeezed states. We then consider a
simple model for a highly relativistic rotating star and show that the
Starobinskii-Unruh effect is absent.Comment: 17 Pages, (accepted by PRD), (previously incorrect header files have
been corrected
Mass Density Perturbations from Inflation with Thermal Dissipation
We study the power spectrum of the mass density perturbations in an inflation
scenario that includes thermal dissipation. We show that the condition on which
the thermal fluctuations dominate the primordial density perturbations can
easily be realized even for weak dissipation, i.e., the rate of dissipation is
less than the Hubble expansion. We find that our spectrum of primordial density
perturbations follows a power law behavior, and exhibits a ``thermodynamical''
feature -- the amplitude and power index of the spectrum depend mainly on the
thermodynamical variable , the inflation energy scale. Comparing this result
with the observed temperature fluctuations of the cosmic microwave background,
we find that both amplitude and index of the power spectrum can be fairly well
fitted if GeV.Comment: 23 pages, 7 figures, REVTex; Phys. Rev. D in pres
Dynamical System Analysis for Inflation with Dissipation
We examine the solutions of the equations of motion for an expanding
Universe, taking into account the radiation of the inflaton field energy. We
then analyze the question of the generality of inflationary solutions in this
more general setting of a dissipative system. We find a surprisingly rich
behavior for the solutions of the dynamical system of equations in the presence
of dissipational effects. We also determine that a value of dissipation as
small as can lead to a smooth exit from inflation to
radiation.Comment: Plain LaTex, 21 pages, 8 eps figs (uses epsf), to be published in
Phys. Rev.
The Rotating Quantum Vacuum
We derive conditions for rotating particle detectors to respond in a variety
of bounded spacetimes and compare the results with the folklore that particle
detectors do not respond in the vacuum state appropriate to their motion.
Applications involving possible violations of the second law of thermodynamics
are briefly addressed.Comment: Plain TeX, 10 pages (to appear in PRD
Inflationary Reheating Classes via Spectral Methods
Inflationary reheating is almost completely controlled by the Floquet
indices, . Using spectral theory we demonstrate that the stability bands
(where ) of the Mathieu and Lam\'e equations are destroyed even in
Minkowski spacetime, leaving a fractal Cantor set or a measure zero set of
stable modes in the cases where the inflaton evolves in an almost-periodic or
stochastic manner respectively. These two types of potential model the expected
multi-field and quantum backreaction effects during reheating.Comment: 5 pages, 2 ps figures, Revtex. Version to appear in Phys. Rev. D
(Rapid Communication, July 15
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