scholarly journals Relative Entropy of Coherent States on General CCR Algebras

2021 ◽  
Author(s):  
Henning Bostelmann ◽  
Daniela Cadamuro ◽  
Simone Del Vecchio
Keyword(s):  
Relative Entropy ◽  
Coherent States ◽  
Regularity Condition ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Boundary Terms ◽  
Ccr Algebra ◽  
Modular Data ◽  
Quasifree State ◽  
Thermal States

AbstractFor a subalgebra of a generic CCR algebra, we consider the relative entropy between a general (not necessarily pure) quasifree state and a coherent excitationthereof. We give a unified formula for this entropy in terms of single-particle modular data. Further, we investigate changes of the relative entropy along subalgebras arising from an increasing family of symplectic subspaces; here convexity of the entropy (as usually considered for the Quantum Null Energy Condition) is replaced with lower estimates for the second derivative, composed of “bulk terms” and “boundary terms”. Our main assumption is that the subspaces are in differential modular position, a regularity condition that generalizes the usual notion of half-sided modular inclusions. We illustrate our results in relevant examples, including thermal states for the conformal U(1)-current.

scholarly journals Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras

2022 ◽  
Author(s):  
Thomas Faulkner ◽  
Stefan Hollands ◽  
Brian Swingle ◽  
Yixu Wang
Keyword(s):  
Relative Entropy ◽  
Von Neumann Algebras ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Reference State ◽  
Type I ◽  
Von Neumann ◽  
Link Type ◽  
Fixed Reference ◽  
Proof Strategy

AbstractWe prove the existence of a universal recovery channel that approximately recovers states on a von Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I von Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary von Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki–Masuda $$L_p$$ L p norms. We comment on applications to the quantum null energy condition.

scholarly journals A Rényi quantum null energy condition: proof for free field theories

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mudassir Moosa ◽  
Pratik Rath ◽  
Vincent Paul Su
Keyword(s):  
Relative Entropy ◽  
Free Field ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Field Theories ◽  
Energy Tensor ◽  
Shape Derivative ◽  
Spacetime Dimension ◽  
Positivity Condition ◽  
Stress Energy

Abstract The Quantum Null Energy Condition (QNEC) is a lower bound on the stress-energy tensor in quantum field theory that has been proved quite generally. It can equivalently be phrased as a positivity condition on the second null shape derivative of the relative entropy Srel(ρ||σ) of an arbitrary state ρ with respect to the vacuum σ. The relative entropy has a natural one-parameter family generalization, the Sandwiched Rényi divergence Sn(ρ||σ), which also measures the distinguishability of two states for arbitrary n ∈ [1/2, ∞). A Rényi QNEC, a positivity condition on the second null shape derivative of Sn(ρ||σ), was conjectured in previous work. In this work, we study the Rényi QNEC for free and superrenormalizable field theories in spacetime dimension d > 2 using the technique of null quantization. In the above setting, we prove the Rényi QNEC in the case n > 1 for arbitrary states. We also provide counterexamples to the Rényi QNEC for n < 1.

scholarly journals Classification of quantum states based on the null energy condition

2021 ◽  
Vol 36 (25) ◽  
pp. 2150183
Author(s):  
Susobhan Mandal
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Coherent States ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Quantum States ◽  
Quantum Field ◽  
Theory Of Relativity ◽  
General Theory Of Relativity

Violation of the null energy condition plays an important role both in the general theory of relativity and quantum field theory in curved spacetimes. Over the years, it has been shown that the violation of the null energy condition leads to instability and violation of causality. In quantum field theory, violation of the energy condition also depends on the quantum states apart from the geometry of curved spacetime. Hence, the quantum effects play an important role in the violation of the null energy condition. We show that the set of all the coherent states does not violate the null energy condition. Further, we also show that under certain conditions, the null energy condition is violated either by a pure state or a mixed state. Furthermore, the dynamical violation of the null energy condition by the quantum states is also discussed here.

scholarly journals ANEC in λϕ4 theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Teresa Bautista ◽  
Lorenzo Casarin ◽  
Hadi Godazgar
Keyword(s):  
Critical Points ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Renormalisation Group ◽  
Quartic Coupling ◽  
Third Order ◽  
Expectation Value ◽  
Scalar State

Abstract Motivated by the goal of applying the average null energy condition (ANEC) to renormalisation group flows, we calculate in λϕ4 theory the expectation value of the ANEC operator in a particular scalar state perturbatively up to third order in the quartic coupling and verify the expected CFT answer. The work provides the technical tools for studying the expectation value of the ANEC operator in more interesting states, for example tensorial states relevant to the Hofman-Maldacena collider bounds, away from critical points.

scholarly journals Singularity Theorems in the Effective Field Theory for Quantum Gravity at Second Order in Curvature

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 171
Author(s):  
Folkert Kuipers ◽  
Xavier Calmet
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Effective Field Theory ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Effective Field ◽  
Second Order ◽  
Jordan Frame ◽  
Singularity Theorems ◽  
Massive Spin

In this paper, we discuss singularity theorems in quantum gravity using effective field theory methods. To second order in curvature, the effective field theory contains two new degrees of freedom which have important implications for the derivation of these theorems: a massive spin-2 field and a massive spin-0 field. Using an explicit mapping of this theory from the Jordan frame to the Einstein frame, we show that the massive spin-2 field violates the null energy condition, while the massive spin-0 field satisfies the null energy condition, but may violate the strong energy condition. Due to this violation, classical singularity theorems are no longer applicable, indicating that singularities can be avoided, if the leading quantum corrections are taken into account.

scholarly journals Wormholes in generalized hybrid metric-Palatini gravity obeying the matter null energy condition everywhere

2018 ◽  
Vol 98 (6) ◽  
Author(s):  
João Luís Rosa ◽  
José P. S. Lemos ◽  
Francisco S. N. Lobo
Keyword(s):  
Energy Condition ◽  
Null Energy Condition

scholarly journals Higher-dimensional evolving wormholes satisfying the null energy condition

2014 ◽  
Vol 90 (2) ◽  
Author(s):  
Mahdi Kord Zangeneh ◽  
Francisco S. N. Lobo ◽  
Nematollah Riazi
Keyword(s):  
Energy Condition ◽  
Null Energy Condition ◽  
Higher Dimensional

scholarly journals Bulk matter and the boundary quantum null energy condition

2018 ◽  
Vol 2018 (8) ◽  
Author(s):  
Zuhair U. Khandker ◽  
Sandipan Kundu ◽  
Daliang Li
Keyword(s):  
Energy Condition ◽  
Null Energy Condition

scholarly journals Possible formation of wormholes from dark matter in an isothermal galactic halo and void

2019 ◽  
Vol 34 (23) ◽  
pp. 1950188
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
P. K. F. Kuhfittig ◽  
G. S. Khadekar
Keyword(s):  
Dark Matter ◽  
Galactic Halo ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Galactic Rotation ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Rotation Curves ◽  
Galactic Rotation Curves ◽  
Traversable Wormholes

It is well-known that traversable wormholes are valid solutions of the Einstein field equations, but these structures can only be maintained by violating the null energy condition. In this paper, we have obtained such wormhole solutions in an isothermal galactic halo, as well as in a void. We have shown that the null energy condition is violated, with the help of a suitable redshift function obtained from flat galactic rotation curves.

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