70,448 research outputs found
Environment-induced uncertainties on moving mirrors in quantum critical theories via holography
Environment effects on a -dimensional mirror from the strongly coupled
d-dimensional quantum critical fields with a dynamic exponent in weakly
squeezed states are studied by the holographic approach. The dual description
is a -dimensional probe brane moving in the -dimensional asymptotic
Lifshitz geometry with gravitational wave perturbations. Using the holographic
influence functional method, we find that the large coupling constant of the
fields reduces the position uncertainty of the mirror, but enhances the
momentum uncertainty. As such, the product of the position and momentum
uncertainties is independent of the coupling constant. The proper choices of
the phase of the squeezing parameter might reduce the uncertainties,
nevertheless large values of its amplitude always lead to the larger
uncertainties due to the fact that more quanta are excited as compared with the
corresponding normal vacuum and thermal states. In the squeezed vacuum state,
the position and momentum of the mirror gain maximum uncertainties from the
field at the dynamic exponent when the same squeezed mode is
considered. As for the squeezed thermal state, the contributions of thermal
fluctuations to the uncertainties decrease as the temperature increases in the
case the contributions increase as the
temperature increases. These results are in sharp contrast with those in the
environments of the relativistic free field. Some possible observable effects
are discussed.Comment: This is the version (v2) published in the Annals of Physic
Time evolution of entanglement entropy of moving mirrors influenced by strongly coupled quantum critical fields
The evolution of the Von Neumann entanglement entropy of a -dimensional
mirror influenced by the strongly coupled -dimensional quantum critical
fields with a dynamic exponent is studied by the holographic approach. The
dual description is a -dimensional probe brane moving in the
-dimensional asymptotic Lifshitz geometry ended at , which plays a
role as the UV energy cutoff. Using the holographic influence functional
method, we find that in the linear response region, by introducing a harmonic
trap for the mirror, which serves as a IR energy cutoff, the Von Neumann
entropy at late times will saturate by a power-law in time for generic values
of and . The saturated value and the relaxation rate depend on the
parameter , which is restricted to but
. We find that the saturated values of the entropy are
qualitatively different for the theories with and .
Additionally, the power law relaxation follows the rate . This probe brane approach provides an alternative way to study
the time evolution of the entanglement entropy in the linear response region
that shows the similar power-law relaxation behavior as in the studies of
entanglement entropies based on Ryu-Takayanagi conjecture. We also compare our
results with quantum Brownian motion in a bath of relativistic free fields.Comment: The published versio
Subvacuum effects in Quantum Critical Theories from Holographic Approach
Subvacuum phenomena on a massive particle induced by a squeezed vacuum state
of strongly coupled critical fields with a dynamical scaling are studied by
employing the holographic approach. The corresponding dual description is the
string moving in the 4+1-dimensional Lifshitz geometry. The squeezed vacuum
state is constructed from the Bogoliubov transformations of the creation and
annihilation operators of the pure vacuum state as a result from the perturbed
geometry. Then the influence on particle's velocity dispersion from the
squeezed vacuum is studied. With appropriate choices of squeezing parameters,
the velocity dispersion is found smaller than the value caused by the normal
vacuum fluctuations. This leads to a subvacuum effect. We find that the
reduction in the velocity dispersion is suppressed by a large coupling constant
of quantum critical fields, but is in principle observable. We then investigate
the effect of the squeezed vacuum to the decoherence dynamics of a quantum
particle. It is found possible for this decoherence to be below the level from
the pure vacuum, rendering another subvacuum phenomenon of recoherence. We make
some estimates of the degree of recoherence, and show that, in contrary to the
velocity dispersion, the recoherence effect is proportional to the large
coupling constant, and can potentially be observed. Finally we make a
comparison with the effect on the particle influenced by a relativistic free
field with the dynamical scaling .Comment: This is the version (v2) published in PR
Notes on Properties of Holographic Strange Metals
We investigate properties of holographic strange metals in -dimensions,
generalizing the analysis performed in arXiv:0912.1061. The bulk spacetime is
-dimensional Lifshitz black hole, while the role of charge carriers is
played by probe D-branes. We mainly focus on massless charge carriers, where
most of the results can be obtained analytically. We obtain exact results for
the free energy and calculate the entropy density, the heat capacity as well as
the speed of sound at low temperature. We obtain the DC conductivity and DC
Hall conductivity and find that the DC conductivity takes a universal form in
the large density limit, while the Hall conductivity is also universal in all
dimensions. We also study the resistivity in different limits and clarify the
condition for the linear dependence on the temperature, which is a key feature
of strange metals. We show that our results for the DC conductivity are
consistent with those obtained via Kubo formula and we obtain the charge
diffusion constant analytically. The corresponding properties of massive charge
carriers are also discussed in brief.Comment: 32 pages, minor modification
A Holographic Description of Negative Energy States
Using the AdS/CFT duality, we study the expectation value of stress tensor in
-dimensional quantum critical theories with a general dynamical scaling
, and explore various constrains on negative energy density for strongly
coupled field theories. The holographic dual theory is the theory of gravity in
3+1-dimensional Lifshitz backgrounds. We adopt a consistent approach to obtain
the boundary stress tensor from bulk construction, which satisfies the trace
Ward identity associated with Lifshitz scaling symmetry. In particular, the
boundary stress tensor, constructed from the gravitational wave deformed
Lifshitz geometry, is found up to second order in gravitational wave
perturbations. {The result} is compared to its counterpart in free {scalar}
field theory at the same order in an expansion of small squeezing parameters.
This allows us to relate the boundary values of gravitational waves to the
squeezing parameters of squeezed vacuum states. We find that, in both cases
with , the stress tensor satisfies the averaged null energy condition, and
is consistent with the quantum interest conjecture. Moreover, the negative
lower bound on null-contracted stress tensor, which is averaged over time-like
trajectories along nearly null directions, is obtained. We find a weaker
constraint on the magnitude and duration of negative null energy density in
strongly coupled field theory as compared with the constraint in free
relativistic field theory. The implications are discussed.Comment: This is the version(v2) published in JHE
Off-equilibrium dynamics of the primordial perturbations in the inflationary universe: the O(N) model
Using the O(N) model as an example, we investigate the self-interaction
effects of inflaton on the dynamics of the primordial perturbations. When
taking interactions into account, it is essential to employ a self-consistent
off-equilibrium formalism to study the evolution of the inflationary background
field and its fluctuations with the back-reaction effects. Within the Hartree
factorization scheme, we show that the O(N) model has at least two observable
remains left behind the off-equilibrium processes: the running spectral index
of primordial density perturbations and the correlations between perturbation
modes in phase space. We find that the running of the spectral index is fully
determined by the rate of the energy transfer from the inflationary background
field to its fluctuations via particle creation processes as well as the
dynamics of the background field itself. Furthermore, the amplitude of the
field fluctuations turns out to be scale-dependent due to the off-equilibrium
evolution. As a consequence, the scale-dependence of fluctuations yields a
correlation between the phase space modes of energy density perturbations,
while the one-point function of the fluctuations in each Hartree mode is still
Gaussian. More importantly, the mode-mode correlation of the primordial
perturbations depends upon the dynamics of the self-interaction {\it as well
as} the initial conditions of the inflation. Hence, we propose that the running
spectral index and the correlation between phase-space modes would be two
observable fossils to probe the epoch of inflation, even beyond.Comment: 22 pages, 8 figure
Perfect digraphs
Let be a digraph. Given a set of vertices , an -path
partition of is a collection of paths of such that
is a partition of and for every . We say that satisfies the
-property if, for every maximum stable set of , there exists an
-path partition of , and we say that is -diperfect if every
induced subdigraph of satisfies the -property. A digraph is an
anti-directed odd cycle if (i) the underlying graph of is a cycle , where and , and (ii) each
of the vertices is either a
source or a sink. Berge (1982) conjectured that a digraph is -diperfect
if, and only if, it contains no induced anti-directed odd cycle. Remark that
this conjecture is strikingly similar to Berge's conjecture on perfect graphs
-- nowadays known as the Strong Perfect Graph Theorem (Chudnovsky, Robertson,
Seymour, and Thomas, 2006). To the best of our knowledge, Berge's conjecture
for -diperfect digraphs has been verified only for symmetric digraphs
and digraphs whose underlying graph are perfect. In this paper, we verify it
for digraphs whose underlying graphs are series-parallel and for
in-semicomplete digraphs. Moreover, we propose a conjecture similar to Berge's
and verify it for all the known cases of Berge's conjecture
Interactive Graphics for Visually Diagnosing Forest Classifiers in R
This paper describes structuring data and constructing plots to explore
forest classification models interactively. A forest classifier is an example
of an ensemble, produced by bagging multiple trees. The process of bagging and
combining results from multiple trees, produces numerous diagnostics which,
with interactive graphics, can provide a lot of insight into class structure in
high dimensions. Various aspects are explored in this paper, to assess model
complexity, individual model contributions, variable importance and dimension
reduction, and uncertainty in prediction associated with individual
observations. The ideas are applied to the random forest algorithm, and to the
projection pursuit forest, but could be more broadly applied to other bagged
ensembles. Interactive graphics are built in R, using the ggplot2, plotly, and
shiny packages
Strange Metallic Behavior in Anisotropic Background
We continue our analysis on conductivity in the anisotropic background by
employing the D-brane probe technique, where the D-branes play the role of
charge carriers. The DC and AC conductivity for massless charge carriers are
obtained analytically, while interesting curves for the AC conductivity are
also plotted. For massive charge carriers, we calculate the DC and AC
conductivities in the dilute limit and we fix the parameters in the
Einstein-Maxwell-dilaton theory so that the background exhibits the same
scaling behaviors as those for real-world strange metals. The DC conductivity
at finite density is also computed.Comment: 24 pages, 2 figures, minor modification
Derivation of hydrodynamics for the gapless mode in the BEC-BCS crossover from the exact one-loop effective action
We show that many hydrodynamical properties of the BEC/BCS crossover in the
presence of a Feshbach resonance at T=0 can be derived easily from the
derivative expansion of the (exact) fully renormalized one-loop effective
action. In particular, we calculate the velocity of sound throughout the BCS
and BEC regimes and derive the generalized superfluid continuity equations for
the composite two-fluid system.Comment: Four pages, 1 figure. Whereas v.2 contained additional references,
but was otherwise unchanged, this new version contains new material
concerning our ability to provide a hydrodynamical description of the BEC/BSC
system. This explains the change of title. Our old results are unaffecte
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