38,295 research outputs found
Simulating adiabatic evolution of gapped spin systems
We show that adiabatic evolution of a low-dimensional lattice of quantum
spins with a spectral gap can be simulated efficiently. In particular, we show
that as long as the spectral gap \Delta E between the ground state and the
first excited state is any constant independent of n, the total number of
spins, then the ground-state expectation values of local operators, such as
correlation functions, can be computed using polynomial space and time
resources. Our results also imply that the local ground-state properties of any
two spin models in the same quantum phase can be efficiently obtained from each
other. A consequence of these results is that adiabatic quantum algorithms can
be simulated efficiently if the spectral gap doesn't scale with n. The
simulation method we describe takes place in the Heisenberg picture and does
not make use of the finitely correlated state/matrix product state formalism.Comment: 13 pages, 2 figures, minor change
Uranus evolution models with simple thermal boundary layers
The strikingly low luminosity of Uranus (Teff ~ Teq) constitutes a
long-standing challenge to our understanding of Ice Giant planets. Here we
present the first Uranus structure and evolution models that are constructed to
agree with both the observed low luminosity and the gravity field data. Our
models make use of modern ab initio equations of state at high pressures for
the icy components water, methane, and ammonia. Proceeding step by step, we
confirm that adiabatic models yield cooling times that are too long, even when
uncertainties in the ice:rock ratio (I:R) are taken into account. We then argue
that the transition between the ice/rock-rich interior and the H/He-rich outer
envelope should be stably stratified. Therefore, we introduce a simple thermal
boundary and adjust it to reproduce the low luminosity. Due to this thermal
boundary, the deep interior of the Uranus models are up to 2--3 warmer than
adiabatic models, necessitating the presence of rocks in the deep interior with
a possible I:R of solar. Finally, we allow for an equilibrium
evolution (Teff ~ Teq) that begun prior to the present day, which would
therefore no longer require the current era to be a "special time" in Uranus'
evolution. In this scenario, the thermal boundary leads to more rapid cooling
of the outer envelope. When Teff ~ Teq is reached, a shallow, subadiabatic zone
in the atmosphere begins to develop. Its depth is adjusted to meet the
luminosity constraint. This work provides a simple foundation for future Ice
Giant structure and evolution models, that can be improved by properly treating
the heat and particle fluxes in the diffusive zones.Comment: 13 pages, Accepted to Icaru
Non-Gaussianities in Multifield Inflation: Superhorizon Evolution, Adiabaticity, and the Fate of fnl
We explore the superhorizon generation of large fnl of the local form in two
field inflation. We calculate the two- and three-point observables in a general
class of potentials which allow for an analytic treatment using the delta N
formalism. Motivated by the conservation of the curvature perturbation outside
the horizon in the adiabatic mode and also by the observed adiabaticity of the
power spectrum, we follow the evolution of fnl^{local} until it is driven into
the adibatic solution by passing through a phase of effectively single field
inflation. We find that although large fnl^{local} may be generated during
inflation, such non-gaussianities are transitory and will be exponentially
damped as the cosmological fluctuations approach adiabaticity.Comment: v3: Typos corrected, minor changes to match published version,
references added, 18 pages, 1 figure. v2: Changed sign of fnl to match WMAP
convention, minor changes throughout, references added, 18 pages, 1 figure.
v1: 17 pages, 1 figur
Particle creation, classicality and related issues in quantum field theory: II. Examples from field theory
We adopt the general formalism, which was developed in Paper I
(arXiv:0708.1233) to analyze the evolution of a quantized time-dependent
oscillator, to address several questions in the context of quantum field theory
in time dependent external backgrounds. In particular, we study the question of
emergence of classicality in terms of the phase space evolution and its
relation to particle production, and clarify some conceptual issues. We
consider a quantized scalar field evolving in a constant electric field and in
FRW spacetimes which illustrate the two extreme cases of late time adiabatic
and highly non-adiabatic evolution. Using the time-dependent generalizations of
various quantities like particle number density, effective Lagrangian etc.
introduced in Paper I, we contrast the evolution in these two limits bringing
out key differences between the Schwinger effect and evolution in the de Sitter
background. Further, our examples suggest that the notion of classicality is
multifaceted and any one single criterion may not have universal applicability.
For example, the peaking of the phase space Wigner distribution on the
classical trajectory \emph{alone} does not imply transition to classical
behavior. An analysis of the behavior of the \emph{classicality parameter},
which was introduced in Paper I, leads to the conclusion that strong particle
production is necessary for the quantum state to become highly correlated in
phase space at late times.Comment: RevTeX 4; 27 pages; 18 figures; second of a series of two papers, the
first being arXiv:0708.1233 [gr-qc]; high resolution figures available from
the authors on reques
Are primordial black holes produced by entropy perturbations in single field inflationary models?
We show that in single field inflationary models the super-horizon evolution
of curvature perturbations on comoving slices , which can cause
the production of primordial black holes (PBH), is not due to entropy
perturbations, but to the background evolution effect on the conversion between
entropy and curvature perturbations. We derive a general relation between the
time derivative of comoving curvature perturbations and entropy perturbations,
in terms of a conversion factor depending on the background evolution. Contrary
to previous results derived in the uniform density gauge assuming the gradient
term can be neglected on super-horizon scales, the relation is valid on any
scale for any minimally coupled single scalar field model, also on sub-horizon
scales where gradient terms are large.
We apply it to the case of quasi-inflection inflation, showing that while
entropy perturbations are decreasing, can grow on super-horizon
scales, due to a large increase of the conversion factor. This happens in the
time interval during which a sufficiently fast decrease of the equation of
state transforms into a growing mode that in slow-roll models would be a
decaying mode. The same mechanism also explains the super-horizon evolution of
in globally adiabatic systems, for which entropy perturbations
vanish on any scale, such as ultra slow-roll inflation and its generalizations
Unified Dark Matter models with fast transition
We investigate the general properties of Unified Dark Matter (UDM) fluid
models where the pressure and the energy density are linked by a barotropic
equation of state (EoS) and the perturbations are adiabatic. The
EoS is assumed to admit a future attractor that acts as an effective
cosmological constant, while asymptotically in the past the pressure is
negligible. UDM models of the dark sector are appealing because they evade the
so-called "coincidence problem" and "predict" what can be interpreted as
, but in general suffer the effects of a non-negligible
Jeans scale that wreak havoc in the evolution of perturbations, causing a large
Integrated Sachs-Wolfe effect and/or changing structure formation at small
scales. Typically, observational constraints are violated, unless the
parameters of the UDM model are tuned to make it indistinguishable from
CDM. Here we show how this problem can be avoided, studying in detail
the functional form of the Jeans scale in adiabatic UDM perturbations and
introducing a class of models with a fast transition between an early
Einstein-de Sitter CDM-like era and a later CDM-like phase. If the
transition is fast enough, these models may exhibit satisfactory structure
formation and CMB fluctuations. To consider a concrete case, we introduce a toy
UDM model and show that it can predict CMB and matter power spectra that are in
agreement with observations for a wide range of parameter values.Comment: 30 pages, 15 figures, JHEP3 style, typos corrected; it matches the
published versio
- …