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

doi:10.1103/PhysRevC.99.054902

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:: Martinez, M.; Schäfer, T.

Publication Date:: 2019-05-06

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.

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                    Martinez, M., & Schäfer, T. Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid.  United States.  doi:10.1103/PhysRevC.99.054902.

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                    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.

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@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}

}

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DOI: 10.1103/PhysRevC.99.054902

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Cited by: 2 works

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

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Works referenced in this record:

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Works referencing / citing this record:

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

Martinez, M.; Schäfer, T.; Skokov, V.
Physical Review D, Vol. 100, Issue 7
DOI: 10.1103/physrevd.100.074017

Figures / Tables found in this record:

Table I (p. 12)

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

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

Abstract

Citation Formats

Figures / Tables:

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

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

Hydrodynamics of R-charged black holes journal, March 2006

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

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

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

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

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

Erratum: Collision-geometry fluctuations and triangular flow in heavy-ion collisions [Phys. Rev. C 81 , 054905 (2010)] journal, September 2010

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

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

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

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

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

Hydrodynamics of R-charged black holes
journal, March 2006

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

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

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

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

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

Erratum: Collision-geometry fluctuations and triangular flow in heavy-ion collisions [Phys. Rev. C 81 , 054905 (2010)]
journal, September 2010

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

How (non-)linear is the hydrodynamics of heavy ion collisions?
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Dynamic universality class of the QCD critical point
journal, September 2004

Bulk viscosity from hydrodynamic fluctuations with relativistic hydrokinetic theory
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Hydrodynamics from charged black branes
journal, January 2011

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

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