Exact time dependence of causal correlations and nonequilibrium density matrices in holographic systems

Joshi, Lata Kh; Mukhopadhyay, Ayan; Preis, Florian; Ramadevi, P.

doi:10.1103/physrevd.96.106006

Cited by 4 publications

(2 citation statements)

References 18 publications

(28 reference statements)

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“…We emphasize that this is not the most general bulk solution for a global quench, and that the details may depend on the specific source that is turned on. However, there is strong numerical and analytic evidence to support the idea that even simple models such as AdS-Vaidya already capture the relevant universal features of the time-evolution and subsequent thermalization after a global quench [35,[77][78][79][80][81]. For example, in the recent paper [81] it was found that the gross features of the correlations following the quench are controlled by just a few parameters: the pump duration and the initial and final temperatures, which are all tuneable in (2.10).…”

Section: Entanglement Entropy After Global Quenchesmentioning

confidence: 99%

Linear response of entanglement entropy from holography

Lokhande

Oling

Pedraza

2017

J. High Energ. Phys.

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For time-independent excited states in conformal field theories, the entanglement entropy of small subsystems satisfies a 'first law'-like relation, in which the change in entanglement is proportional to the energy within the entangling region. Such a law holds for time-dependent scenarios as long as the state is perturbatively close to the vacuum, but is not expected otherwise. In this paper we use holography to investigate the spread of entanglement entropy for unitary evolutions of special physical interest, the so-called global quenches. We model these using AdS-Vaidya geometries. We find that the first law of entanglement is replaced by a linear response relation, in which the energy density takes the role of the source and is integrated against a time-dependent kernel with compact support. For adiabatic quenches the standard first law is recovered, while for rapid quenches the linear response includes an extra term that encodes the process of thermalization. This extra term has properties that resemble a time-dependent 'relative entropy'. We propose that this quantity serves as a useful order parameter to characterize far-fromequilibrium excited states. We illustrate our findings with concrete examples, including generic power-law and periodically driven quenches.

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Section: Entanglement Entropy After Global Quenchesmentioning

confidence: 99%

Linear response of entanglement entropy from holography

Lokhande

Oling

Pedraza

2017

J. High Energ. Phys.

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“…See[44] for the non-equilibrium retarded correlation function in a hydrodynamic expansion, and[45,46] for AdS-Vaidya and states corresponding to quenches, etc. The latter uses the prescription of[10].…”

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confidence: 99%

Correlation functions of the Bjorken flow in the holographic Schwinger-Keldysh approach

Banerjee¹,

Mitra²,

Mukhopadhyay³

2022

Preprint

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One of the outstanding problems in the holographic approach to many-body physics is the explicit computation of correlation functions of non-equilibrium states. In this work, we develop the method to compute the Schwinger-Keldysh correlation functions in a holographic theory in the limit in which the state hydrodynamizes, i.e. when the stress tensor is well described by the hydrodynamic effective theory, in the context of the Bjorken flow. Firstly, we provide a new and simple proof that the horizon cap prescription of Crossley-Glorioso-Liu for implementing the thermal Schwinger-Keldysh contour in the bulk is consistent with the KMS periodicity and the ingoing boundary condition for the retarded propagator at any arbitrary frequency and momentum. The generalization to the hydrodynamic Bjorken flow is achieved by a Weyl rescaling in which the dual black hole's event horizon attains constant surface gravity and area at late time, implying constant temperature and entropy density for the dual state (instead of perfect fluid expansion) at large proper time although the directions longitudinal and transverse to the flow expands and contract respectively implying eternal absence of time-translation symmetry. Undoing the Weyl rescaling, the correlation functions can be computed systematically in the large proper time expansion. Remarkably, the horizon cap has to be pinned to the non-equilibrium event horizon so that regularity and consistency conditions are satisfied. This mirrors the causal nature of Schwinger-Dyson equations in field theory. One of our key results is that in the limit of perfect fluid expansion, the Schwinger-Keldysh correlation functions are simply thermal at an appropriate temperature when expressed in terms of reparametrized spacetime arguments. A generalized bi-local thermal structure holds to all orders. We argue that the Stokes data (which are functions rather than constants) for the hydrodynamic correlation functions can decode the quantum fluctuations behind the horizon cap pinned to the evolving event horizon, and thus the details of the initial state.

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Out of equilibrium chiral vortical effect in holography

Morales-Tejera

Landsteiner

2020

Phys. Rev. D

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Exact time dependence of causal correlations and nonequilibrium density matrices in holographic systems

Cited by 4 publications

References 18 publications

Linear response of entanglement entropy from holography

Linear response of entanglement entropy from holography

Correlation functions of the Bjorken flow in the holographic Schwinger-Keldysh approach

Out of equilibrium chiral vortical effect in holography

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