Saturation of the quantum null energy condition in far-from-equilibrium systems

Ecker, Christian; Grumiller, Daniel; van der Schee, Wilke; Stanzer, Philipp

doi:10.1103/PhysRevD.97.126016

Title: Saturation of the quantum null energy condition in far-from-equilibrium systems

Abstract

The quantum null energy condition (QNEC) is a new local energy condition that a general quantum field theory (QFT) is believed to satisfy, relating the classical null energy condition (NEC) to the second functional derivative of the entanglement entropy in the corresponding null direction. We present the first series of explicit computations of QNEC in a strongly coupled QFT, using holography. Here we consider the vacuum, thermal equilibrium, a homogeneous far-from-equilibrium quench as well as a colliding system that violates NEC. For the vacuum and thermal phase, QNEC is always weaker than NEC. While for the homogeneous quench QNEC is satisfied with a finite gap, we find the interesting result that the colliding system can saturate QNEC, depending on the null direction.

Authors:: Ecker, Christian; Grumiller, Daniel; van der Schee, Wilke; Stanzer, Philipp

Publication Date:: 2018-06-25

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1457076

Alternate Identifier(s):: OSTI ID: 1501456

Grant/Contract Number:: SC0011090

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 12; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Ecker, Christian, Grumiller, Daniel, van der Schee, Wilke, and Stanzer, Philipp. Saturation of the quantum null energy condition in far-from-equilibrium systems.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.97.126016.

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                    Ecker, Christian, Grumiller, Daniel, van der Schee, Wilke, & Stanzer, Philipp. Saturation of the quantum null energy condition in far-from-equilibrium systems.  United States.  https://doi.org/10.1103/PhysRevD.97.126016

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                    Ecker, Christian, Grumiller, Daniel, van der Schee, Wilke, and Stanzer, Philipp. Mon .  
"Saturation of the quantum null energy condition in far-from-equilibrium systems".  United States.  https://doi.org/10.1103/PhysRevD.97.126016.

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@article{osti_1457076,

  title        = {Saturation of the quantum null energy condition in far-from-equilibrium systems},

  author       = {Ecker, Christian and Grumiller, Daniel and van der Schee, Wilke and Stanzer, Philipp},

  abstractNote = {The quantum null energy condition (QNEC) is a new local energy condition that a general quantum field theory (QFT) is believed to satisfy, relating the classical null energy condition (NEC) to the second functional derivative of the entanglement entropy in the corresponding null direction. We present the first series of explicit computations of QNEC in a strongly coupled QFT, using holography. Here we consider the vacuum, thermal equilibrium, a homogeneous far-from-equilibrium quench as well as a colliding system that violates NEC. For the vacuum and thermal phase, QNEC is always weaker than NEC. While for the homogeneous quench QNEC is satisfied with a finite gap, we find the interesting result that the colliding system can saturate QNEC, depending on the null direction.},

  doi          = {10.1103/PhysRevD.97.126016},

  journal      = {Physical Review D},

  number       = 12,

  volume       = 97,

  place        = {United States},

  year         = {2018},

  month        = {6}

}

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FIG. 1. : Two families of extremal surfaces at representative locations (t_L, y_L) = (0.75,± 0.5) for the shock-wave geometry. The families correspond to a null variation at a point where the classical NEC is violated (purple region at z = 0 or black region in Fig. 6). The familymore »

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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

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

Gauge theory correlators from non-critical string theory
journal, May 1998

Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M.
Physics Letters B, Vol. 428, Issue 1-2
DOI: 10.1016/S0370-2693(98)00377-3

Holographic proof of the quantum null energy condition
journal, July 2016

Koeller, Jason; Leichenauer, Stefan
Physical Review D, Vol. 94, Issue 2
DOI: 10.1103/PhysRevD.94.024026

The quantum null energy condition in curved space
journal, October 2017

Fu, Zicao; Koeller, Jason; Marolf, Donald
Classical and Quantum Gravity, Vol. 34, Issue 22
DOI: 10.1088/1361-6382/aa8f2c

Deriving covariant holographic entanglement
journal, November 2016

Dong, Xi; Lewkowycz, Aitor; Rangamani, Mukund
Journal of High Energy Physics, Vol. 2016, Issue 11
DOI: 10.1007/JHEP11(2016)028

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

Local modular Hamiltonians from the quantum null energy condition
journal, March 2018

Koeller, Jason; Leichenauer, Stefan; Levine, Adam
Physical Review D, Vol. 97, Issue 6
DOI: 10.1103/PhysRevD.97.065011

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006

Ryu, Shinsei; Takayanagi, Tadashi
Physical Review Letters, Vol. 96, Issue 18
DOI: 10.1103/PhysRevLett.96.181602

The large $N$ limit of superconformal field theories and supergravity
journal, January 1998

Maldacena, Juan
Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2
DOI: 10.4310/ATMP.1998.v2.n2.a1

Anti de Sitter space and holography
journal, January 1998

Witten, Edward
Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2
DOI: 10.4310/ATMP.1998.v2.n2.a2

Modular Hamiltonians on the null plane and the Markov property of the vacuum state
journal, August 2017

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo
Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 36
DOI: 10.1088/1751-8121/aa7eaa

Averaged energy conditions and quantum inequalities
journal, April 1995

Ford, L. H.; Roman, Thomas A.
Physical Review D, Vol. 51, Issue 8
DOI: 10.1103/PhysRevD.51.4277

The Singularities of Gravitational Collapse and Cosmology
journal, January 1970

Hawking, S. W.; Penrose, R.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 314, Issue 1519
DOI: 10.1098/rspa.1970.0021

Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy
journal, November 2014

Wall, Aron C.
Classical and Quantum Gravity, Vol. 31, Issue 22
DOI: 10.1088/0264-9381/31/22/225007

The quantum interest conjecture
journal, October 1999

Ford, L. H.; Roman, Thomas A.
Physical Review D, Vol. 60, Issue 10
DOI: 10.1103/PhysRevD.60.104018

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

Evolution of holographic entanglement entropy in an anisotropic system
journal, July 2015

Ecker, Christian; Grumiller, Daniel; Stricker, Stefan A.
Journal of High Energy Physics, Vol. 2015, Issue 7
DOI: 10.1007/JHEP07(2015)146

Lower Bound on the Energy Density in Classical and Quantum Field Theories
journal, April 2017

Wall, Aron C.
Physical Review Letters, Vol. 118, Issue 15
DOI: 10.1103/PhysRevLett.118.151601

Holography and Colliding Gravitational Shock Waves in Asymptotically $Ad S_{5}$ Spacetime
journal, January 2011

Chesler, Paul M.; Yaffe, Laurence G.
Physical Review Letters, Vol. 106, Issue 2
DOI: 10.1103/PhysRevLett.106.021601

Absence of a local rest frame in far from equilibrium quantum matter
journal, October 2014

Arnold, Peter; Romatschke, Paul; van der Schee, Wilke
Journal of High Energy Physics, Vol. 2014, Issue 10
DOI: 10.1007/JHEP10(2014)110

A covariant holographic entanglement entropy proposal
journal, July 2007

Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi
Journal of High Energy Physics, Vol. 2007, Issue 07
DOI: 10.1088/1126-6708/2007/07/062

Generalized gravitational entropy
journal, August 2013

Lewkowycz, Aitor; Maldacena, Juan
Journal of High Energy Physics, Vol. 2013, Issue 8
DOI: 10.1007/JHEP08(2013)090

Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes
journal, July 2014

Chesler, Paul M.; Yaffe, Laurence G.
Journal of High Energy Physics, Vol. 2014, Issue 7
DOI: 10.1007/JHEP07(2014)086

Exploring nonlocal observables in shock wave collisions
journal, November 2016

Ecker, Christian; Grumiller, Daniel; Stanzer, Philipp
Journal of High Energy Physics, Vol. 2016, Issue 11
DOI: 10.1007/JHEP11(2016)054

On the collision of two shock waves in AdS ₅
journal, August 2008

Grumiller, Daniel; Romatschke, Paul
Journal of High Energy Physics, Vol. 2008, Issue 08
DOI: 10.1088/1126-6708/2008/08/027

Corrigendum: The quantum null energy condition in curved space (2017 Class. Quantum Grav . 34 225012)
journal, January 2018

Fu, Zicao; Koeller, Jason; Marolf, Donald
Classical and Quantum Gravity, Vol. 35, Issue 4
DOI: 10.1088/1361-6382/aaa5c9

Strong subadditivity and the covariant holographic entanglement entropy formula
journal, June 2012

Callan, Robert; He, Jianyang; Headrick, Matthew
Journal of High Energy Physics, Vol. 2012, Issue 6
DOI: 10.1007/JHEP06(2012)081

Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence
journal, March 2001

de Haro, Sebastian; Skenderis, Kostas; Solodukhin, Sergey N.
Communications in Mathematical Physics, Vol. 217, Issue 3
DOI: 10.1007/s002200100381

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

Entropy production in collisions of gravitational shock waves and of heavy ions
journal, September 2008

Gubser, Steven S.; Pufu, Silviu S.; Yarom, Amos
Physical Review D, Vol. 78, Issue 6
DOI: 10.1103/PhysRevD.78.066014

Modeling heavy ion collisions in AdS/CFT
journal, July 2008

Albacete, Javier L.; Kovchegov, Yuri V.; Taliotis, Anastasios
Journal of High Energy Physics, Vol. 2008, Issue 07
DOI: 10.1088/1126-6708/2008/07/100

Non-local observables at finite temperature in AdS/CFT
journal, March 2018

Erdmenger, Johanna; Miekley, Nina
Journal of High Energy Physics, Vol. 2018, Issue 3
DOI: 10.1007/JHEP03(2018)034

Holographic evolution of entanglement entropy
journal, November 2010

Abajo-Arrastia, Javier; Aparício, João; López, Esperanza
Journal of High Energy Physics, Vol. 2010, Issue 11
DOI: 10.1007/JHEP11(2010)149

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

From Full Stopping to Transparency in a Holographic Model of Heavy Ion Collisions
journal, October 2013

Casalderrey-Solana, Jorge; Heller, Michal P.; Mateos, David
Physical Review Letters, Vol. 111, Issue 18
DOI: 10.1103/PhysRevLett.111.181601

Strongly coupled gauge theories: high and low temperature behavior of non-local observables
journal, May 2013

Fischler, Willy; Kundu, Sandipan
Journal of High Energy Physics, Vol. 2013, Issue 5
DOI: 10.1007/JHEP05(2013)098

Works referencing / citing this record:

Energy density from second shape variations of the von Neumann entropy
journal, October 2018

Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin
Physical Review D, Vol. 98, Issue 8
DOI: 10.1103/physrevd.98.086013

Local Quantum Energy Conditions in Non-Lorentz-Invariant Quantum Field Theories
journal, September 2019

Grumiller, Daniel; Parekh, Pulastya; Riegler, Max
Physical Review Letters, Vol. 123, Issue 12
DOI: 10.1103/physrevlett.123.121602

Quantum null energy condition and its (non)saturation in 2d CFTs
journal, January 2019

Ecker, Christian; Grumiller, Daniel; van der Schee, Wilke
SciPost Physics, Vol. 6, Issue 3
DOI: 10.21468/scipostphys.6.3.036

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Title: Saturation of the quantum null energy condition in far-from-equilibrium systems

Abstract

Citation Formats

Figures / Tables:

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

Averaged null energy condition from causality journal, July 2017

Gauge theory correlators from non-critical string theory journal, May 1998

Holographic proof of the quantum null energy condition journal, July 2016

The quantum null energy condition in curved space journal, October 2017

Deriving covariant holographic entanglement journal, November 2016

Quantum focusing conjecture journal, March 2016

Local modular Hamiltonians from the quantum null energy condition journal, March 2018

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence journal, May 2006

The large $N$ limit of superconformal field theories and supergravity journal, January 1998

Anti de Sitter space and holography journal, January 1998

Modular Hamiltonians on the null plane and the Markov property of the vacuum state journal, August 2017

Averaged energy conditions and quantum inequalities journal, April 1995

The Singularities of Gravitational Collapse and Cosmology journal, January 1970

Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy journal, November 2014

The quantum interest conjecture journal, October 1999

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

Evolution of holographic entanglement entropy in an anisotropic system journal, July 2015

Lower Bound on the Energy Density in Classical and Quantum Field Theories journal, April 2017

Holography and Colliding Gravitational Shock Waves in Asymptotically Ad S 5 Spacetime journal, January 2011

Absence of a local rest frame in far from equilibrium quantum matter journal, October 2014

A covariant holographic entanglement entropy proposal journal, July 2007

Generalized gravitational entropy journal, August 2013

Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes journal, July 2014

Exploring nonlocal observables in shock wave collisions journal, November 2016

On the collision of two shock waves in AdS 5 journal, August 2008

Corrigendum: The quantum null energy condition in curved space (2017 Class. Quantum Grav . 34 225012) journal, January 2018

Strong subadditivity and the covariant holographic entanglement entropy formula journal, June 2012

Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence journal, March 2001

Proof of the quantum null energy condition journal, January 2016

Entropy production in collisions of gravitational shock waves and of heavy ions journal, September 2008

Modeling heavy ion collisions in AdS/CFT journal, July 2008

Non-local observables at finite temperature in AdS/CFT journal, March 2018

Holographic evolution of entanglement entropy journal, November 2010

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

From Full Stopping to Transparency in a Holographic Model of Heavy Ion Collisions journal, October 2013

Strongly coupled gauge theories: high and low temperature behavior of non-local observables journal, May 2013

Energy density from second shape variations of the von Neumann entropy journal, October 2018

Local Quantum Energy Conditions in Non-Lorentz-Invariant Quantum Field Theories journal, September 2019

Quantum null energy condition and its (non)saturation in 2d CFTs journal, January 2019

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

Averaged null energy condition from causality
journal, July 2017

Gauge theory correlators from non-critical string theory
journal, May 1998

Holographic proof of the quantum null energy condition
journal, July 2016

The quantum null energy condition in curved space
journal, October 2017

Deriving covariant holographic entanglement
journal, November 2016

Quantum focusing conjecture
journal, March 2016

Local modular Hamiltonians from the quantum null energy condition
journal, March 2018

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006

The large $N$ limit of superconformal field theories and supergravity
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Anti de Sitter space and holography
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Modular Hamiltonians on the null plane and the Markov property of the vacuum state
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Averaged energy conditions and quantum inequalities
journal, April 1995

The Singularities of Gravitational Collapse and Cosmology
journal, January 1970

Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy
journal, November 2014

The quantum interest conjecture
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Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
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Evolution of holographic entanglement entropy in an anisotropic system
journal, July 2015

Lower Bound on the Energy Density in Classical and Quantum Field Theories
journal, April 2017

Holography and Colliding Gravitational Shock Waves in Asymptotically $Ad S_{5}$ Spacetime
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Absence of a local rest frame in far from equilibrium quantum matter
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A covariant holographic entanglement entropy proposal
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Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes
journal, July 2014

Exploring nonlocal observables in shock wave collisions
journal, November 2016

On the collision of two shock waves in AdS ₅
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Corrigendum: The quantum null energy condition in curved space (2017 Class. Quantum Grav . 34 225012)
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Strong subadditivity and the covariant holographic entanglement entropy formula
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Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence
journal, March 2001

Proof of the quantum null energy condition
journal, January 2016

Entropy production in collisions of gravitational shock waves and of heavy ions
journal, September 2008

Modeling heavy ion collisions in AdS/CFT
journal, July 2008

Non-local observables at finite temperature in AdS/CFT
journal, March 2018

Holographic evolution of entanglement entropy
journal, November 2010

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

From Full Stopping to Transparency in a Holographic Model of Heavy Ion Collisions
journal, October 2013

Strongly coupled gauge theories: high and low temperature behavior of non-local observables
journal, May 2013

Energy density from second shape variations of the von Neumann entropy
journal, October 2018

Local Quantum Energy Conditions in Non-Lorentz-Invariant Quantum Field Theories
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