skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid

Abstract

We investigate the impact of hydrodynamic fluctuations on correlation functions in a scale invariant fluid with a conserved U(1) charge. The kinetic equations for the two-point functions of pressure, momentum, and heat energy densities are derived within the framework of stochastic hydrodynamics. The leading nonanalytic contributions to the energy-momentum tensor as well as the U(1) current are determined from the solutions to these kinetic equations. In the case of a static homogeneous background we show that the long time tails obtained from hydrokinetic equations reproduce the one-loop results derived from statistical field theory. We use these results to establish bounds on transport coefficients. We generalize the stochastic equation to a background flow undergoing Bjorken expansion. We compute the leading fractional power O((τT)–3/2) correction to the U(1) current and compare with the first-order gradient term.

Authors:
;
Publication Date:
Research Org.:
North Carolina State Univ., Raleigh, NC (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1511074
Alternate Identifier(s):
OSTI ID: 1511003
Grant/Contract Number:  
FG02-03ER41260
Resource Type:
Published Article
Journal Name:
Physical Review C
Additional Journal Information:
Journal Name: Physical Review C Journal Volume: 99 Journal Issue: 5; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Hydrodynamic fluctuations; Stochastic Hydrodynamics

Citation Formats

Martinez, M., and Schäfer, T. Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid. United States: N. p., 2019. Web. doi:10.1103/PhysRevC.99.054902.
Martinez, M., & Schäfer, T. Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid. United States. doi:10.1103/PhysRevC.99.054902.
Martinez, M., and Schäfer, T. Mon . "Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid". United States. doi:10.1103/PhysRevC.99.054902.
@article{osti_1511074,
title = {Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid},
author = {Martinez, M. and Schäfer, T.},
abstractNote = {We investigate the impact of hydrodynamic fluctuations on correlation functions in a scale invariant fluid with a conserved U(1) charge. The kinetic equations for the two-point functions of pressure, momentum, and heat energy densities are derived within the framework of stochastic hydrodynamics. The leading nonanalytic contributions to the energy-momentum tensor as well as the U(1) current are determined from the solutions to these kinetic equations. In the case of a static homogeneous background we show that the long time tails obtained from hydrokinetic equations reproduce the one-loop results derived from statistical field theory. We use these results to establish bounds on transport coefficients. We generalize the stochastic equation to a background flow undergoing Bjorken expansion. We compute the leading fractional power O((τT)–3/2) correction to the U(1) current and compare with the first-order gradient term.},
doi = {10.1103/PhysRevC.99.054902},
journal = {Physical Review C},
number = 5,
volume = 99,
place = {United States},
year = {2019},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevC.99.054902

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Figures / Tables:

Table I Table I: Renormalized thermodynamic variables and transport coefficients due to hydrodynamic fluctuations in different approaches.

Save / Share:

Works referenced in this record:

Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity
journal, February 2013


Collision-geometry fluctuations and triangular flow in heavy-ion collisions
journal, May 2010


Fluid dynamics of R-charged black holes
journal, January 2009


Relativistic viscous hydrodynamics, conformal invariance, and holography
journal, April 2008


Characterization of initial fluctuations for the hydrodynamical description of heavy ion collisions
journal, October 2013


Relativistic theory of hydrodynamic fluctuations with applications to heavy-ion collisions
journal, May 2012


Gaussian stochastic processes in physics
journal, December 1978


Statistics of initial density perturbations in heavy ion collisions and their fluid dynamic response
journal, August 2014

  • Floerchinger, Stefan; Wiedemann, Urs Achim
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)005

Statistical Dynamics of Classical Systems
journal, July 1973


A cumulant expansion for stochastic linear differential equations. I
journal, June 1974


Thermodynamical second-order hydrodynamic coefficients
journal, November 2012

  • Moore, Guy D.; Sohrabi, Kiyoumars A.
  • Journal of High Energy Physics, Vol. 2012, Issue 11
  • DOI: 10.1007/JHEP11(2012)148

Hydrodynamics of R-charged black holes
journal, March 2006


Initial conditions for hydrodynamics from weakly coupled pre-equilibrium evolution
journal, August 2016

  • Keegan, Liam; Kurkela, Aleksi; Mazeliauskas, Aleksas
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)171

Hydrodynamic fluctuations of entropy in one-dimensionally expanding system
journal, April 2019


Reciprocal Relations in Irreversible Processes. I.
journal, February 1931


Kubo Formulas for Second-Order Hydrodynamic Coefficients
journal, March 2011


Matching the Nonequilibrium Initial Stage of Heavy Ion Collisions to Hydrodynamics with QCD Kinetic Theory
journal, March 2019


Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions
journal, March 2019

  • Kurkela, Aleksi; Mazeliauskas, Aleksas; Paquet, Jean-François
  • Physical Review C, Vol. 99, Issue 3
  • DOI: 10.1103/PhysRevC.99.034910

Kubo formulas for the shear and bulk viscosity relaxation times and the scalar field theory shear τ π calculation
journal, June 2017


Second order hydrodynamic coefficients from kinetic theory
journal, March 2009


Lectures on hydrodynamic fluctuations in relativistic theories
journal, November 2012


Hydrodynamic fluctuations, long-time tails, and supersymmetry
journal, July 2003


Stickiness of sound: An absolute lower limit on viscosity and the breakdown of second-order relativistic hydrodynamics
journal, July 2011


Quasinormal modes and holography
journal, October 2005


Hydrodynamic Fluctuations in Relativistic Heavy-Ion Collisions
journal, February 2019


Fluctuations around Bjorken flow and the onset of turbulent phenomena
journal, November 2011

  • Floerchinger, Stefan; Wiedemann, Urs Achim
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)100

Theory of Diffusive Fluctuations
journal, March 2019


Hydrodynamic equations and correlation functions
journal, October 1963


Theory of dynamic critical phenomena
journal, July 1977


Reciprocal Relations in Irreversible Processes. II.
journal, December 1931


Introduction to hydrodynamics
journal, October 2015


Hydrodynamic tails and a fluctuation bound on the bulk viscosity
journal, December 2017


Mode-by-mode fluid dynamics for relativistic heavy ion collisions
journal, January 2014


Kinetic freeze-out, particle spectra, and harmonic-flow coefficients from mode-by-mode hydrodynamics
journal, March 2014


Nonlinear fluid dynamics from gravity
journal, February 2008

  • Bhattacharyya, Sayantani; Minwalla, Shiraz; Hubeny, Veronika E.
  • Journal of High Energy Physics, Vol. 2008, Issue 02
  • DOI: 10.1088/1126-6708/2008/02/045

Impact of resonance decays on critical point signals in net-proton fluctuations
journal, April 2017


Time dependent correlation functions and mode-mode coupling theories
journal, June 1975


How (non-)linear is the hydrodynamics of heavy ion collisions?
journal, July 2014


Dynamic universality class of the QCD critical point
journal, September 2004


Bulk viscosity from hydrodynamic fluctuations with relativistic hydrokinetic theory
journal, February 2018


Hydrodynamics from charged black branes
journal, January 2011

  • Banerjee, Nabamita; Bhattacharya, Jyotirmoy; Bhattacharyya, Sayantani
  • Journal of High Energy Physics, Vol. 2011, Issue 1
  • DOI: 10.1007/JHEP01(2011)094

Fluid dynamic propagation of initial baryon number perturbations on a Bjorken flow background
journal, December 2015


Real-time evolution of non-Gaussian cumulants in the QCD critical regime
journal, September 2015


Hydrodynamics with parametric slowing down and fluctuations near the critical point
journal, August 2018


Implications of hydrodynamic fluctuations for the minimum shear viscosity of the dilute Fermi gas at unitarity
journal, May 2013


Relativistic second-order dissipative hydrodynamics at finite chemical potential
journal, December 2015


Fluctuation bounds on charge and heat diffusion
journal, June 2015


Kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
journal, January 2017


Signatures of the Tricritical Point in QCD
journal, November 1998


    Works referencing / citing this record:

    Critical behavior of the bulk viscosity in QCD
    journal, October 2019


      Figures / Tables found in this record:

        Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.