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

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

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1103/PhysRevD.97.126016

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1. FIG. 1. : Two families of extremal surfaces at representative locations (tL, yL) = (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 » starting at y = −0.5 hovers just above the apparent horizon (colored surface) and hence has larger entropy, as well as more negative S00 (right Fig., see also Fig. 8).« less

Save / Share:

Works referenced in this record:

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


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


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


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


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

  • 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


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


The quantum interest conjecture
journal, October 1999


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


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

  • 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


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


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

  • 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


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


    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


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


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