Holographic Brownian motion in $$2+1$$ 2 + 1 dimensional hairy black holes

Sadeghi, J.; Pourhassan, B.; Pourasadollah, F.

doi:10.1140/epjc/s10052-014-2793-7

Cited by 26 publications

(18 citation statements)

References 39 publications

(91 reference statements)

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“…In the case of the charged hairy black hole, relation with a charged extremal black hole as well as charged non-extremal black hole has been discussed. Holographic description of such solutions has been considered to study Brownian motion [4], and found similar behavior with the asymptotic uncharged case in the low frequency limit. Thermodynamics and statistics of these black holes at special limits investigated by recent literatures [5,6,9,10,11].…”

Section: Introductionmentioning

confidence: 76%

The Klein–Gordon equation of a rotating charged hairy black hole in (2 + 1) dimensions

Pourhassan

2016

Mod. Phys. Lett. A

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In this paper, we consider the Klein-Gordon equation in a 3D charged rotating hairy black hole background to study behavior of a massive scalar field. In the general case we find periodic-like behavior for the scalar field which may be vanishes at the black hole horizon or far from the black hole horizon. For the special cases of non-rotating or near horizon approximation we find radial solution of Klein-Gordon equation in terms of hypergeometric and Kummer functions. Also for the case of uncharged black hole we find numerical solution of the Klein-Gordon equation as periodic function which may enhanced out of the black hole or vanish at horizon. We find allowed boundary conditions which yield to the identical bosons described by scalar field.

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Section: Introductionmentioning

confidence: 76%

The Klein–Gordon equation of a rotating charged hairy black hole in (2 + 1) dimensions

Pourhassan

2016

Mod. Phys. Lett. A

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“…The applicability of our effective theory framework to the scenario where the bath is chaotic and strongly coupled implies that it may be possible to construct a holographic dual description [61][62][63][64][65][66][67][68][69] of the particle's non-linear dynamics. The OTO extension of this nonlinear dynamics may be useful in determining a holographic prescription for computing the particle's OTOCs [67,70].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Out of time ordered effective dynamics of a quartic oscillator

Chakrabarty

Chaudhuri

2019

SciPost Phys.

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We study the dynamics of a quantum Brownian particle weakly coupled to a thermal bath. Working in the Schwinger-Keldysh formalism, we develop an effective action of the particle up to quartic terms. We demonstrate that this quartic effective theory is dual to a stochastic dynamics governed by a non-linear Langevin equation. The Schwinger-Keldysh effective theory, or the equivalent non-linear Langevin dynamics, is insufficient to determine the out of time order correlators (OTOCs) of the particle. To overcome this limitation, we construct an extended effective action in a generalised Schwinger-Keldysh framework. We determine the additional quartic couplings in this OTO effective action and show their dependence on the bath's 4-point OTOCs. We analyse the constraints imposed on the OTO effective theory by microscopic reversibility and thermality of the bath. We show that these constraints lead to a generalised fluctuation-dissipation relation between the non-Gaussianity in the distribution of the thermal noise experienced by the particle and the thermal jitter in its damping coefficient. The quartic effective theory developed in this work provides extension of several results previously obtained for the cubic OTO dynamics of a Brownian particle. Contents SciPost PhysicsSubmission [22,[27][28][29]. Nevertheless, it is interesting to explore the corrections to this effective dynamics by including the cubic and higher degree terms in the analysis. A simple way to obtain such corrections is to extend the Caldeira-Leggett model by introducing a non-linear combination of the bath oscillators' positions in the operator that couples to the particle [29,30].One such extension was discussed in [30] where the oscillators in the bath were divided into two sets (labelled by X and Y). Then apart from the bilinear interactions (which are present in the Caldeira-Leggett model), small cubic interactions were introduced between the particle (q) and pairs of bath oscillators. Each such pair consisted of one oscillator drawn from the set X and the other from the set Y. Due to these cubic interactions, this model was called the 'qXY model'.Introduction of these cubic interactions leads to cubic and higher degree terms in the effective action of the particle. In [30], this effective theory was studied up to the cubic terms in a Markovian limit. It was shown to be dual to a non-linear Langevin dynamics which has perturbative corrections over the linear Langevin dynamics in the Caldeira-Leggett model. The additional parameters in this non-linear dynamics receive contributions from the 3-point correlators of the bath. These 3-point correlators lead to an anharmonicity in the particle's dynamics and a non-Gaussianity in the distribution of the thermal noise experienced by the particle. In addition, they also give rise to thermal jitters 1 in both the frequency and the damping of the particle. The thermal jitter in the damping coefficient and the non-Gaussianity in the noise are connected by a generalised fluctuation-dissipation relation [30...

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“…In the Ref. [11] a charged black hole with a scalar field which is coupled to gravity in (2 + 1)-dimensions [12,13,14,15,16] considered and logarithmic corrections to the corresponding system using two approaches computed. In that case the effects of thermal fluctuations on a charged AdS black hole has been investigated by [17].…”

Section: Introductionmentioning

confidence: 99%

Quantum loop corrections of a charged de Sitter black hole

Naji

2018

Annals of Physics

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Holographic Brownian motion in $$2+1$$ 2 + 1 dimensional hairy black holes

Cited by 26 publications

References 39 publications

The Klein–Gordon equation of a rotating charged hairy black hole in (2 + 1) dimensions

The Klein–Gordon equation of a rotating charged hairy black hole in (2 + 1) dimensions

Out of time ordered effective dynamics of a quartic oscillator

Quantum loop corrections of a charged de Sitter black hole

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