Thermalization, viscosity and the averaged null energy condition

Delacrétaz, Luca V.; Hartman, Thomas; Hartnoll, Sean A.; Lewkowycz, Aitor

doi:10.1007/JHEP10(2018)028

Title: Thermalization, viscosity and the averaged null energy condition

Abstract

We explore the implications of the averaged null energy condition for thermal states of relativistic quantum field theories. A key property of such thermal states is the thermalization length. This lengthscale generalizes the notion of a mean free path beyond weak coupling, and allows finite size regions to independently thermalize. Using the eigenstate thermalization hypothesis, we show that thermal fluctuations in finite size 'fireballs' can produce states that violate the averaged null energy condition if the thermalization length is too short or if the shear viscosity is too large. These bounds become very weak with a large number N of degrees of freedom but can constrain real-world systems, such as the quark-gluon plasma.

Authors:

Delacrétaz, Luca V. ^[1]; Hartman, Thomas ^[2]; Hartnoll, Sean A. ^[1]; Lewkowycz, Aitor ^[1]

Stanford Univ., CA (United States). Department of Physics
Cornell Univ., Ithaca, NY (United States). Department of Physics

Publication Date:: 2018-10-04

Research Org.:: Cornell Univ., Ithaca, NY (United States); Stanford Univ., CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1483478

Grant/Contract Number:: SC0014123; SC0018134

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 10; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quark-Gluon Plasma; Effective Field Theories

Citation Formats


                    Delacrétaz, Luca V., Hartman, Thomas, Hartnoll, Sean A., and Lewkowycz, Aitor. Thermalization, viscosity and the averaged null energy condition.  United States: N. p., 2018. 
Web.  doi:10.1007/JHEP10(2018)028.

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                    Delacrétaz, Luca V., Hartman, Thomas, Hartnoll, Sean A., & Lewkowycz, Aitor. Thermalization, viscosity and the averaged null energy condition.  United States.  https://doi.org/10.1007/JHEP10(2018)028

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                    Delacrétaz, Luca V., Hartman, Thomas, Hartnoll, Sean A., and Lewkowycz, Aitor. Thu .  
"Thermalization, viscosity and the averaged null energy condition".  United States.  https://doi.org/10.1007/JHEP10(2018)028.  https://www.osti.gov/servlets/purl/1483478.

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@article{osti_1483478,

  title        = {Thermalization, viscosity and the averaged null energy condition},

  author       = {Delacrétaz, Luca V. and Hartman, Thomas and Hartnoll, Sean A. and Lewkowycz, Aitor},

  abstractNote = {We explore the implications of the averaged null energy condition for thermal states of relativistic quantum field theories. A key property of such thermal states is the thermalization length. This lengthscale generalizes the notion of a mean free path beyond weak coupling, and allows finite size regions to independently thermalize. Using the eigenstate thermalization hypothesis, we show that thermal fluctuations in finite size 'fireballs' can produce states that violate the averaged null energy condition if the thermalization length is too short or if the shear viscosity is too large. These bounds become very weak with a large number N of degrees of freedom but can constrain real-world systems, such as the quark-gluon plasma.},

  doi          = {10.1007/JHEP10(2018)028},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 10,

  volume       = 2018,

  place        = {United States},

  year         = {2018},

  month        = {10}

}

Copy to clipboard

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Works referenced in this record:

Constraints on parity violating conformal field theories in d = 3
journal, November 2017

Chowdhury, Subham Dutta; David, Justin R.; Prakash, Shiroman
Journal of High Energy Physics, Vol. 2017, Issue 11
DOI: 10.1007/JHEP11(2017)171

Averaged energy conditions for free scalar fields in flat spacetime
journal, April 1991

Klinkhammer, Gunnar
Physical Review D, Vol. 43, Issue 8
DOI: 10.1103/PhysRevD.43.2542

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

Baier, Rudolf; Romatschke, Paul; Son, Dam Thanh
Journal of High Energy Physics, Vol. 2008, Issue 04
DOI: 10.1088/1126-6708/2008/04/100

Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008

Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim
Nature, Vol. 452, Issue 7189
DOI: 10.1038/nature06838

Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
journal, March 2005

Kovtun, P. K.; Son, D. T.; Starinets, A. O.
Physical Review Letters, Vol. 94, Issue 11
DOI: 10.1103/PhysRevLett.94.111601

Calculation of the Bulk Viscosity in SU(3) Gluodynamics
journal, April 2008

Meyer, Harvey B.
Physical Review Letters, Vol. 100, Issue 16
DOI: 10.1103/PhysRevLett.100.162001

Universality of long-distance AdS physics from the CFT bootstrap
journal, August 2014

Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.
Journal of High Energy Physics, Vol. 2014, Issue 8
DOI: 10.1007/JHEP08(2014)145

A bound on chaos
journal, August 2016

Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
Journal of High Energy Physics, Vol. 2016, Issue 8
DOI: 10.1007/JHEP08(2016)106

Quantum critical transport, duality, and M theory
journal, April 2007

Herzog, Christopher P.; Kovtun, Pavel; Sachdev, Subir
Physical Review D, Vol. 75, Issue 8
DOI: 10.1103/PhysRevD.75.085020

Does a Single Eigenstate Encode the Full Hamiltonian?
journal, April 2018

Garrison, James R.; Grover, Tarun
Physical Review X, Vol. 8, Issue 2
DOI: 10.1103/PhysRevX.8.021026

Averaged null energy condition from causality
journal, July 2017

Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein
Journal of High Energy Physics, Vol. 2017, Issue 7
DOI: 10.1007/JHEP07(2017)066

Higher derivative gravity, causality and positivity of energy in a UV complete QFT
journal, December 2009

Hofman, Diego M.
Nuclear Physics B, Vol. 823, Issue 1-2
DOI: 10.1016/j.nuclphysb.2009.08.001

From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
journal, May 2016

D'Alessio, Luca; Kafri, Yariv; Polkovnikov, Anatoli
Advances in Physics, Vol. 65, Issue 3
DOI: 10.1080/00018732.2016.1198134

Universal bounds on operator dimensions from the average null energy condition
journal, February 2018

Córdova, Clay; Diab, Kenan
Journal of High Energy Physics, Vol. 2018, Issue 2
DOI: 10.1007/JHEP02(2018)131

A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
journal, September 2018

Romero-Bermúdez, Aurelio; Sabella-Garnier, Philippe; Schalm, Koenraad
Journal of High Energy Physics, Vol. 2018, Issue 9
DOI: 10.1007/JHEP09(2018)005

Plate with a hole obeys the averaged null energy condition
journal, July 2005

Graham, Noah; Olum, Ken D.
Physical Review D, Vol. 72, Issue 2
DOI: 10.1103/PhysRevD.72.025013

Probing beyond ETH at large c
journal, June 2018

Faulkner, Thomas; Wang, Huajia
Journal of High Energy Physics, Vol. 2018, Issue 6
DOI: 10.1007/JHEP06(2018)123

On CFT and quantum chaos
journal, December 2016

Turiaci, Gustavo J.; Verlinde, Herman
Journal of High Energy Physics, Vol. 2016, Issue 12
DOI: 10.1007/JHEP12(2016)110

QGP viscosity at RHIC and the LHC – a 2012 status report
journal, May 2013

Song, Huichao
Nuclear Physics A, Vol. 904-905
DOI: 10.1016/j.nuclphysa.2013.01.052

Quantum focusing conjecture
journal, March 2016

Bousso, Raphael; Fisher, Zachary; Leichenauer, Stefan
Physical Review D, Vol. 93, Issue 6
DOI: 10.1103/PhysRevD.93.064044

Theory of universal incoherent metallic transport
journal, December 2014

Hartnoll, Sean A.
Nature Physics, Vol. 11, Issue 1
DOI: 10.1038/nphys3174

Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories
journal, July 2018

Hikida, Yasuaki; Kusuki, Yuya; Takayanagi, Tadashi
Physical Review D, Vol. 98, Issue 2
DOI: 10.1103/PhysRevD.98.026003

Upper Bound on Diffusivity
journal, October 2017

Hartman, Thomas; Hartnoll, Sean A.; Mahajan, Raghu
Physical Review Letters, Vol. 119, Issue 14
DOI: 10.1103/PhysRevLett.119.141601

Viscosity, Black Holes, and Quantum Field Theory
journal, November 2007

Son, Dam T.; Starinets, Andrei O.
Annual Review of Nuclear and Particle Science, Vol. 57, Issue 1
DOI: 10.1146/annurev.nucl.57.090506.123120

Early thermalization at RHIC
journal, May 2002

Heinz, U.; Kolb, P.
Nuclear Physics A, Vol. 702, Issue 1-4
DOI: 10.1016/S0375-9474(02)00714-5

The QCD equation of state with dynamical quarks
journal, November 2010

Borsányi, Szabolcs; Endrődi, Gergely; Fodor, Zoltán
Journal of High Energy Physics, Vol. 2010, Issue 11
DOI: 10.1007/JHEP11(2010)077

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
journal, September 2016

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
Journal of High Energy Physics, Vol. 2016, Issue 9
DOI: 10.1007/JHEP09(2016)038

Lectures on hydrodynamic fluctuations in relativistic theories
journal, November 2012

Kovtun, Pavel
Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 47
DOI: 10.1088/1751-8113/45/47/473001

Multipoint correlators of conformal field theories: Implications for quantum critical transport
journal, February 2013

Chowdhury, Debanjan; Raju, Suvrat; Sachdev, Subir
Physical Review B, Vol. 87, Issue 8
DOI: 10.1103/PhysRevB.87.085138

QCD equation of state with almost physical quark masses
journal, January 2008

Cheng, M.; Christ, N. H.; Datta, S.
Physical Review D, Vol. 77, Issue 1
DOI: 10.1103/PhysRevD.77.014511

Hadron spectra and elliptic flow for 200 $A$ GeV $Au + Au$ collisions from viscous hydrodynamics coupled to a Boltzmann cascade
journal, May 2011

Song, Huichao; Bass, Steffen A.; Heinz, Ulrich
Physical Review C, Vol. 83, Issue 5
DOI: 10.1103/PhysRevC.83.054910

Conformal collider physics: energy and charge correlations
journal, May 2008

Hofman, Diego M.; Maldacena, Juan
Journal of High Energy Physics, Vol. 2008, Issue 05
DOI: 10.1088/1126-6708/2008/05/012

Geodesic focusing, energy conditions and singularities
journal, March 1987

Borde, A.
Classical and Quantum Gravity, Vol. 4, Issue 2
DOI: 10.1088/0264-9381/4/2/015

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

Kovtun, Pavel; Moore, Guy D.; Romatschke, Paul
Physical Review D, Vol. 84, Issue 2
DOI: 10.1103/PhysRevD.84.025006

Subsystem eigenstate thermalization hypothesis
journal, January 2018

Dymarsky, Anatoly; Lashkari, Nima; Liu, Hong
Physical Review E, Vol. 97, Issue 1
DOI: 10.1103/PhysRevE.97.012140

Proof of the quantum null energy condition
journal, January 2016

Bousso, Raphael; Fisher, Zachary; Koeller, Jason
Physical Review D, Vol. 93, Issue 2
DOI: 10.1103/PhysRevD.93.024017

Quantum stress-energy tensors and the weak energy condition
journal, June 1986

Roman, Thomas A.
Physical Review D, Vol. 33, Issue 12
DOI: 10.1103/PhysRevD.33.3526

Quantum statistical mechanics in a closed system
journal, February 1991

Deutsch, J. M.
Physical Review A, Vol. 43, Issue 4
DOI: 10.1103/PhysRevA.43.2046

Chaos and quantum thermalization
journal, August 1994

Srednicki, Mark
Physical Review E, Vol. 50, Issue 2
DOI: 10.1103/PhysRevE.50.888

The Shear Viscosity to Entropy Ratio: a Status Report
journal, September 2011

Cremonini, Sera
Modern Physics Letters B, Vol. 25, Issue 23
DOI: 10.1142/S0217984911027315

Solving the 3D Ising model with the conformal bootstrap
journal, July 2012

El-Showk, Sheer; Paulos, Miguel F.; Poland, David
Physical Review D, Vol. 86, Issue 2
DOI: 10.1103/PhysRevD.86.025022

The conformal bootstrap
journal, June 2016

Poland, David; Simmons-Duffin, David
Nature Physics, Vol. 12, Issue 6
DOI: 10.1038/nphys3761

Bounds on OPE coefficients from interference effects in the conformal collider
journal, November 2017

Córdova, Clay; Maldacena, Juan; Turiaci, Gustavo J.
Journal of High Energy Physics, Vol. 2017, Issue 11
DOI: 10.1007/JHEP11(2017)032

Holographic entanglement entropy from 2d CFT: heavy states and local quenches
journal, February 2015

Asplund, Curtis T.; Bernamonti, Alice; Galli, Federico
Journal of High Energy Physics, Vol. 2015, Issue 2
DOI: 10.1007/JHEP02(2015)171

The 3d stress-tensor bootstrap
journal, February 2018

Dymarsky, Anatoly; Kos, Filip; Kravchuk, Petr
Journal of High Energy Physics, Vol. 2018, Issue 2
DOI: 10.1007/JHEP02(2018)164

Works referencing / citing this record:

Fast conformal bootstrap and constraints on 3d gravity
journal, May 2019

Afkhami-Jeddi, Nima; Hartman, Thomas; Tajdini, Amirhossein
Journal of High Energy Physics, Vol. 2019, Issue 5
DOI: 10.1007/jhep05(2019)087

Fast Conformal Bootstrap and Constraints on 3d Gravity
text, January 2019

Afkhami-Jeddi, Nima; Hartman, Thomas; Tajdini, Amirhossein
arXiv
DOI: 10.48550/arxiv.1903.06272

Strongly coupled electron fluids in the Poiseuille regime
text, January 2018

Erdmenger, Johanna; Matthaiakakis, Ioannis; Meyer, Rene
arXiv
DOI: 10.48550/arxiv.1806.10635

Strongly coupled electron fluids in the Poiseuille regime
journal, November 2018

Erdmenger, Johanna; Matthaiakakis, Ioannis; Meyer, René
Physical Review B, Vol. 98, Issue 19
DOI: 10.1103/physrevb.98.195143

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Similar Records

Title: Thermalization, viscosity and the averaged null energy condition

Abstract

Citation Formats

Constraints on parity violating conformal field theories in d = 3 journal, November 2017

Averaged energy conditions for free scalar fields in flat spacetime journal, April 1991

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

Thermalization and its mechanism for generic isolated quantum systems journal, April 2008

Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics journal, March 2005

Calculation of the Bulk Viscosity in SU(3) Gluodynamics journal, April 2008

Universality of long-distance AdS physics from the CFT bootstrap journal, August 2014

A bound on chaos journal, August 2016

Quantum critical transport, duality, and M theory journal, April 2007

Does a Single Eigenstate Encode the Full Hamiltonian? journal, April 2018

Averaged null energy condition from causality journal, July 2017

Higher derivative gravity, causality and positivity of energy in a UV complete QFT journal, December 2009

From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics journal, May 2016

Universal bounds on operator dimensions from the average null energy condition journal, February 2018

A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled journal, September 2018

Plate with a hole obeys the averaged null energy condition journal, July 2005

Probing beyond ETH at large c journal, June 2018

On CFT and quantum chaos journal, December 2016

QGP viscosity at RHIC and the LHC – a 2012 status report journal, May 2013

Quantum focusing conjecture journal, March 2016

Theory of universal incoherent metallic transport journal, December 2014

Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories journal, July 2018

Upper Bound on Diffusivity journal, October 2017

Viscosity, Black Holes, and Quantum Field Theory journal, November 2007

Early thermalization at RHIC journal, May 2002

The QCD equation of state with dynamical quarks journal, November 2010

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition journal, September 2016

Lectures on hydrodynamic fluctuations in relativistic theories journal, November 2012

Multipoint correlators of conformal field theories: Implications for quantum critical transport journal, February 2013

QCD equation of state with almost physical quark masses journal, January 2008

Hadron spectra and elliptic flow for 200 A GeV Au + Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade journal, May 2011

Conformal collider physics: energy and charge correlations journal, May 2008

Geodesic focusing, energy conditions and singularities journal, March 1987

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

Subsystem eigenstate thermalization hypothesis journal, January 2018

Proof of the quantum null energy condition journal, January 2016

Quantum stress-energy tensors and the weak energy condition journal, June 1986

Quantum statistical mechanics in a closed system journal, February 1991

Chaos and quantum thermalization journal, August 1994

The Shear Viscosity to Entropy Ratio: a Status Report journal, September 2011

Solving the 3D Ising model with the conformal bootstrap journal, July 2012

The conformal bootstrap journal, June 2016

Bounds on OPE coefficients from interference effects in the conformal collider journal, November 2017

Holographic entanglement entropy from 2d CFT: heavy states and local quenches journal, February 2015

The 3d stress-tensor bootstrap journal, February 2018

Fast conformal bootstrap and constraints on 3d gravity journal, May 2019

Fast Conformal Bootstrap and Constraints on 3d Gravity text, January 2019

Strongly coupled electron fluids in the Poiseuille regime text, January 2018

Strongly coupled electron fluids in the Poiseuille regime journal, November 2018

Constraints on parity violating conformal field theories in d = 3
journal, November 2017

Averaged energy conditions for free scalar fields in flat spacetime
journal, April 1991

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

Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008

Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
journal, March 2005

Calculation of the Bulk Viscosity in SU(3) Gluodynamics
journal, April 2008

Universality of long-distance AdS physics from the CFT bootstrap
journal, August 2014

A bound on chaos
journal, August 2016

Quantum critical transport, duality, and M theory
journal, April 2007

Does a Single Eigenstate Encode the Full Hamiltonian?
journal, April 2018

Averaged null energy condition from causality
journal, July 2017

Higher derivative gravity, causality and positivity of energy in a UV complete QFT
journal, December 2009

From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
journal, May 2016

Universal bounds on operator dimensions from the average null energy condition
journal, February 2018

A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
journal, September 2018

Plate with a hole obeys the averaged null energy condition
journal, July 2005

Probing beyond ETH at large c
journal, June 2018

On CFT and quantum chaos
journal, December 2016

QGP viscosity at RHIC and the LHC – a 2012 status report
journal, May 2013

Quantum focusing conjecture
journal, March 2016

Theory of universal incoherent metallic transport
journal, December 2014

Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories
journal, July 2018

Upper Bound on Diffusivity
journal, October 2017

Viscosity, Black Holes, and Quantum Field Theory
journal, November 2007

Early thermalization at RHIC
journal, May 2002

The QCD equation of state with dynamical quarks
journal, November 2010

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
journal, September 2016

Lectures on hydrodynamic fluctuations in relativistic theories
journal, November 2012

Multipoint correlators of conformal field theories: Implications for quantum critical transport
journal, February 2013

QCD equation of state with almost physical quark masses
journal, January 2008

Hadron spectra and elliptic flow for 200 $A$ GeV $Au + Au$ collisions from viscous hydrodynamics coupled to a Boltzmann cascade
journal, May 2011

Conformal collider physics: energy and charge correlations
journal, May 2008

Geodesic focusing, energy conditions and singularities
journal, March 1987

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

Subsystem eigenstate thermalization hypothesis
journal, January 2018

Proof of the quantum null energy condition
journal, January 2016

Quantum stress-energy tensors and the weak energy condition
journal, June 1986

Quantum statistical mechanics in a closed system
journal, February 1991

Chaos and quantum thermalization
journal, August 1994

The Shear Viscosity to Entropy Ratio: a Status Report
journal, September 2011

Solving the 3D Ising model with the conformal bootstrap
journal, July 2012

The conformal bootstrap
journal, June 2016

Bounds on OPE coefficients from interference effects in the conformal collider
journal, November 2017

Holographic entanglement entropy from 2d CFT: heavy states and local quenches
journal, February 2015

The 3d stress-tensor bootstrap
journal, February 2018

Fast conformal bootstrap and constraints on 3d gravity
journal, May 2019

Fast Conformal Bootstrap and Constraints on 3d Gravity
text, January 2019

Strongly coupled electron fluids in the Poiseuille regime
text, January 2018

Strongly coupled electron fluids in the Poiseuille regime
journal, November 2018