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

Christian Ecker,Wilke Van Der Schee,Daniel Grumiller,Philipp Stanzer

doi:10.1103/physrevd.97.126016

Christian Ecker, Wilke Van Der Schee + Show 2 more

Open Access

https://doi.org/10.1103/physrevd.97.126016

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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. We consider the vacuum, thermal equilibrium, a homogeneous far-from-equilibrium quench as well as a colliding system that violates NEC. For vacuum and the 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.

Highlights

Energy conditions rose to prominence in the 1960s as requisites for proofs of singularity theorems or Hawking’s area theorem [1,2]
While for the homogeneous quench quantum null energy condition (QNEC) is satisfied with a finite gap, we find the interesting result that the colliding system can saturate QNEC, depending on the null direction
Our main result is the saturation of QNEC in far-from-equilibrium regions created during shock-wave collisions

Summary

INTRODUCTION

Energy conditions rose to prominence in the 1960s as requisites for proofs of singularity theorems or Hawking’s area theorem [1,2]. Our work relies on previous work in numerical relativity that determined the time-evolution of holographic entanglement entropy (HEE) [23] and extracted features of interest for thermalization of anisotropic systems [24] or holographic models of non-Abelian plasma formation in heavy ion collisions [25] based on a geometric setup that considers the collision of gravitational shock waves [26,27,28] numerically [29,30,31] This latter setup has the interesting property that for sufficiently localized shock waves NEC (1) is violated [26,30] with remarkable consequences for phenomenology, such as the absence of a local rest frame in far from equilibrium quantum matter [32]. We consider physical systems of increasing complexity before addressing colliding gravitational shock waves, where we discover a surprising saturation of the QNEC inequality (2), depending on the null direction kμ used therein

COMPUTING QNEC

Thermal plasma

Far-from-equilibrium quench

Shock-wave collision

DISCUSSION