1,580 research outputs found
Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
Consistent formulations of relativistic viscous hydrodynamics involve short
lived modes, leading to asymptotic rather than convergent gradient expansions.
In this Letter we consider the Mueller-Israel-Stewart theory applied to a
longitudinally expanding quark-gluon plasma system and identify hydrodynamics
as a universal attractor without invoking the gradient expansion. We give
strong evidence for the existence of this attractor and then show that it can
be recovered from the divergent gradient expansion by Borel summation. This
requires careful accounting for the short-lived modes which leads to an
intricate mathematical structure known from the theory of resurgence.Comment: Presentation improved, typos fixed; roughly matches the published
versio
How does relativistic kinetic theory remember about initial conditions?
Understanding hydrodynamization in microscopic models of heavy-ion collisions
has been an important topic in current research. Many lessons obtained within
the strongly-coupled (holographic) models originate from the properties of
transient excitations of equilibrium encapsulated by short-lived quasinormal
modes of black holes. This paper aims to develop similar intuition for
expanding plasma systems described by a simple model from the weakly-coupled
domain, the Boltzmann equation in the relaxation time approximation. We show
that in this kinetic theory setup there are infinitely many transient modes
carrying information about the initial distribution function. They all have the
same exponential damping set by the relaxation time but are distinguished by
different power-law suppressions and different frequencies of oscillations,
logarithmic in proper time. We also analyze the resurgent interplay between the
hydrodynamics and transients in this setup.Comment: 11 pages, 4 figures; Published in Physical Review
Hydrodynamization in kinetic theory: Transient modes and the gradient expansion
We explore the transition to hydrodynamics in a weakly-coupled model of
quark-gluon plasma given by kinetic theory in the relaxation time approximation
with conformal symmetry. We demonstrate that the gradient expansion in this
model has a vanishing radius of convergence due to the presence of a transient
(nonhydrodynamic) mode, in a way similar to results obtained earlier in
strongly-coupled gauge theories. This suggests that the mechanism by which
hydrodynamic behaviour emerges is the same, which we further corroborate by a
novel comparison between solutions of different weakly and strongly coupled
models. However, in contrast with other known cases, we find that not all the
singularities of the analytic continuation of the Borel transform of the
gradient expansion correspond to transient excitations of the microscopic
system: some of them reflect analytic properties of the kinetic equation when
the proper time is continued to complex values.Comment: 6 pages, 2 figures, v2: author added, major rewrite, mysterious off
real axis singularities in the Borel plane explained (!), see also
arXiv:1802.08225 [nucl-th] by Heller and Svensson; v3: references added,
minor improvements in the text, first 426 terms from Eq. (8) included in the
submission; v4: title changed, matches published versio
Coupling hydrodynamics to nonequilibrium degrees of freedom in strongly interacting quark-gluon plasma
Relativistic hydrodynamics simulations of quark-gluon plasma play a pivotal
role in our understanding of heavy ion collisions at RHIC and LHC. They are
based on a phenomenological description due to Mueller, Israel, Stewart (MIS)
and others, which incorporates viscous effects and ensures a well-posed initial
value problem. Focusing on the case of conformal plasma we propose a
generalization which includes, in addition, the dynamics of the least damped
far-from-equilibrium degree of freedom found in strongly coupled plasmas
through the AdS/CFT correspondence. We formulate new evolution equations for
general flows and then test them in the case of N=4 super Yang-Mills plasma by
comparing their solutions alongside solutions of MIS theory with numerical
computations of isotropization and boost-invariant flow based on holography. In
these tests the new equations reproduce the results of MIS theory when
initialized close to the hydrodynamic stage of evolution, but give a more
accurate description of the dynamics when initial conditions are set in the
pre-equilibrium regime.Comment: Minor improvements; references adde
Entropy Production, Hydrodynamics, and Resurgence in the Primordial Quark-Gluon Plasma from Holography
Microseconds after the Big Bang quarks and gluons formed a strongly-coupled
non-conformal liquid driven out-of-equilibrium by the expansion of the
Universe. We use holography to determine the non-equilibrium behavior of this
liquid in a Friedmann-Lemaitre-Robertson-Walker Universe and develop an
expansion for the corresponding entropy production in terms of the derivatives
of the cosmological scale factor. We show that the resulting series has zero
radius of convergence and we discuss its resurgent properties. Finally, we
compute the resummed entropy production rate in de Sitter Universe at late
times and show that the leading order approximation given by bulk viscosity
effects can strongly overestimate/underestimate the rate depending on the
microscopic parameters.Comment: 7 pages, 1 figure; v2: various improvements in presentation, title
changed by journal, matches the published versio
Hydrodynamic gradient expansion in gauge theory plasmas
We utilize the fluid-gravity duality to investigate the large order behavior
of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma
system. This corresponds to the inclusion of dissipative terms and transport
coefficients of very high order. Using the dual gravity description, we
calculate numerically the form of the stress tensor for a boost-invariant flow
in a hydrodynamic expansion up to terms with 240 derivatives. We observe a
factorial growth of gradient contributions at large orders, which indicates a
zero radius of convergence of the hydrodynamic series. Furthermore, we identify
the leading singularity in the Borel transform of the hydrodynamic energy
density with the lowest nonhydrodynamic excitation corresponding to a
`nonhydrodynamic' quasinormal mode on the gravity side.Comment: v2: 4+2 pages, 2 figures, title changed by journal, supplemental
material incorporated into the preprint, energy density coefficients up to
240th order included in the submission (change in normalization with respect
to v1), matches published versio
sQGP as hCFT
We examine the proposal to make quantitative comparisons between the strongly
coupled quark-gluon plasma and holographic descriptions of conformal field
theory. In this note, we calculate corrections to certain transport
coefficients appearing in second-order hydrodynamics from higher curvature
terms to the dual gravity theory. We also clarify how these results might be
consistently applied in comparisons with the sQGP.Comment: 13 page
Equilibration rates in a strongly coupled nonconformal quark-gluon plasma
We initiate the study of equilibration rates of strongly coupled quark-gluon
plasmas in the absence of conformal symmetry. We primarily consider a
supersymmetric mass deformation within gauge theory and use
holography to compute quasinormal modes of a variety of scalar operators, as
well as the energy-momentum tensor. In each case, the lowest quasinormal
frequency, which provides an approximate upper bound on the thermalization
time, is proportional to temperature, up to a pre-factor with only a mild
temperature dependence. We find similar behaviour in other holographic plasmas,
where the model contains an additional scale beyond the temperature. Hence, our
study suggests that the thermalization time is generically set by the
temperature, irrespective of any other scales, in strongly coupled gauge
theories.Comment: 6 pages, 7 figure
Towards Complexity for Quantum Field Theory States
We investigate notions of complexity of states in continuous quantum-many
body systems. We focus on Gaussian states which include ground states of free
quantum field theories and their approximations encountered in the context of
the continuous version of Multiscale Entanglement Renormalization Ansatz. Our
proposal for quantifying state complexity is based on the Fubini-Study metric.
It leads to counting the number of applications of each gate (infinitesimal
generator) in the transformation, subject to a state-dependent metric. We
minimize the defined complexity with respect to momentum preserving quadratic
generators which form algebras. On the manifold of
Gaussian states generated by these operations the Fubini-Study metric
factorizes into hyperbolic planes with minimal complexity circuits reducing to
known geodesics. Despite working with quantum field theories far outside the
regime where Einstein gravity duals exist, we find striking similarities
between our results and holographic complexity proposals.Comment: 6+7 pages, 6 appendices, 2 figures; v2: references added;
acknowledgments expanded; appendix F added, reviewing similarities and
differences with hep-th/1707.08570; v3: version published in PR
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