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

Field-induced collective spin-exciton condensation in a quasi-2D dx2-y2-wave heavy electron superconductor

The origin of the spin resonance observed in CeCoIn5 with Inelastic Neutron Scattering is subject to debate. It has been shown recently that in this heavy electron compound at low temperature an instability to a ground state with coexisting dx2 -y2 -wave superconductivity and Spin Density Wave (SDW) order in a magnetic field is a corollary of the consideration of a collective spin excitation mode in a quasi-2D dx2 -y2 -wave Pauli-limited superconductor. This provides a natural scenario for the occurence of the puzzling high-field-low-temperature phase highlighted in CeCoIn5 . We present perspectives on this ground state transition and propose directions for future experiment.Comment: SCES 2011 proceedin

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

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

Muon Spin Rotation in Heavy Electron Pauli Limited Superconductors

The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli limited heavy electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to Muon Spin Rotation ($\mu$SR) experiment. On the basis of the Ginzburg-Landau expansion for the superconductor free energy we study the evolution with respect to external field of the static linewidth both in the limit of independent vortices (low magnetic field) and in the near $H_\mathrm{c2}^\mathrm{p}(T)$ regime by using an extension of the Abrikosov analysis to Pauli limited superconductors. We conclude that in the Ginzburg-Landau regime with Pauli limit, the electrodynamics of the vortex lattice predicts anomalous variations with applied field of the static linewidth which is a result of the spin response contribution to screening supercurrents that dominates the usual charge response. The model is proposed as a benchmark for comparison with possible other effects including vortex core localized states or interplay with magnetism

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

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