Charge diffusion and the butterfly effect in striped holographic matter

Lucas, Andrew; Steinberg, Julia

doi:10.1007/jhep10(2016)143

Cited by 76 publications

(90 citation statements)

References 93 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the coherent regime, the mixing term M (2.4) is important and (ζ, χ) should be taken into account so the energy diffusion constant in the coherent regime will not be universal. By the same reason the charge diffusion constant may not be universal and this non-universality was also observed in [22,24,25] and it seems that chaos is only connected to energy diffusion [18,22]. Therefore, it is an interesting future direction to search a velocity scale for charge diffusion.…”

Section: Jhep06(2017)030mentioning

confidence: 98%

“…More evidence for the energy diffusion bound (D e /v 2 B ) was shown in holographic models that flow to AdS 2 ×R d fixed points in the infrared in [20] and in the Sachdev-Ye-Kitaev (SYK) models [21][22][23]. 4 However, it was shown that charge diffusion (D c /v 2 B ) may not have a universal lower bound in striped holographic matter [24] and in the SYK model [22]. When the higher derivative correction is added the energy diffusion (D e /v 2 B ) still can have a lower bound while the charge diffusion (D c /v 2 B ) may vanish depending on the higher derivative couplings [25].…”

Section: Jhep06(2017)030mentioning

confidence: 99%

See 1 more Smart Citation

Diffusion and butterfly velocity at finite density

Niu

Kim

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

Abstract:We study diffusion and butterfly velocity (v B ) in two holographic models, linear axion and axion-dilaton model, with a momentum relaxation parameter (β) at finite density or chemical potential (µ). Axion-dilaton model is particularly interesting since it shows linear-T -resistivity, which may have something to do with the universal bound of diffusion. At finite density, there are two diffusion constants D ± describing the coupled diffusion of charge and energy. By computing D ± exactly, we find that in the incoherent regime (β/T 1, β/µ 1) D + is identified with the charge diffusion constant (D c ) and D − is identified with the energy diffusion constant (D e ). In the coherent regime, at very small density, D ± are 'maximally' mixed in the sense that D + (D − ) is identified with D e (D c ), which is opposite to the case in the incoherent regime. In the incoherent regime D e ∼ C − v 2 B /k B T where C − = 1/2 or 1 so it is universal independently of β and µ. However, D c ∼ C + v 2 B /k B T where C + = 1 or β 2 /16π 2 T 2 so, in general, C + may not saturate to the lower bound in the incoherent regime, which suggests that the characteristic velocity for charge diffusion may not be the butterfly velocity. We find that the finite density does not affect the diffusion property at zero density in the incoherent regime.

show abstract

Section: Jhep06(2017)030mentioning

confidence: 98%

Section: Jhep06(2017)030mentioning

confidence: 99%

Diffusion and butterfly velocity at finite density

Niu

Kim

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…One remarkable example that saturates this bound is the Sachdev-Ye-Kitaev (SYK) model [10,18]. Recently, the butterfly velocity v B has also been conjectured as the characteristic velocity that universally bounds the diffusion constants in incoherent metal [15][16][17]19]. Since in holographic theories the bound in (1.2) is always saturated, we will focus on the behavior of the butterfly velocity close to quantum critical points (QCP).…”

Section: Jhep10(2017)025mentioning

confidence: 99%

“…Very importantly, as a characteristic velocity of a chaotic quantum system, v B sets a bound on the speed of the information propagation [1]. In holographic theories, the butterfly effect has extensively been studied in context [5][6][7][8][9][10][11][12][13][14][15][16][17]. In the study of high energy scattering near horizon and information scrambling of black holes it is found that the butterfly effect ubiquitously exists and is signaled by a…”

Section: Introductionmentioning

confidence: 99%

Holographic butterfly effect at quantum critical points

Ling¹,

Liu²,

Wu³

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

When the Lyapunov exponent λ L in a quantum chaotic system saturates the bound λ L 2πk B T , it is proposed that this system has a holographic dual described by a gravity theory. In particular, the butterfly effect as a prominent phenomenon of chaos can ubiquitously exist in a black hole system characterized by a shockwave solution near the horizon. In this paper we propose that the butterfly velocity can be used to diagnose quantum phase transition (QPT) in holographic theories. We provide evidences for this proposal with an anisotropic holographic model exhibiting metal-insulator transitions (MIT), in which the derivatives of the butterfly velocity with respect to system parameters characterizes quantum critical points (QCP) with local extremes in zero temperature limit. We also point out that this proposal can be tested by experiments in the light of recent progress on the measurement of out-of-time-order correlation function (OTOC).

show abstract

“…However, motivated by recent experimental progress [3][4][5], there has been considerable theoretical work using hydrodynamics to study thermoelectric transport [2,[6][7][8][9][10][11][12][13][14][15][16][17][18] and it is therefore of interest to see how our general results on diffusion manifest themselves in this particular context. More specifically, we will study this within the context of relativistic hydrodynamics, describing the hydrodynamic limit of a relativistic quantum field theory.…”

Section: Introductionmentioning

confidence: 99%

Diffusion in inhomogeneous media

2017

View full text Add to dashboard Cite

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyze the retarded two-point functions involving the charges and the associated currents at long wavelengths, compared to the scale of the lattice, and, when the dc conductivities are finite, extract the hydrodynamic modes associated with diffusion of the charges. We show that the dispersion relations of these modes are related to the eigenvalues of a specific matrix constructed from the dc conductivities and certain thermodynamic susceptibilities, thus obtaining generalized Einstein relations. We illustrate these general results in the specific context of relativistic hydrodynamics where translation invariance is broken using spatially inhomogeneous and periodic deformations of the stress tensor and the conserved Uð1Þ currents. Equivalently, this corresponds to considering hydrodynamics on a curved manifold, with a spatially periodic metric and chemical potential, and we obtain the dispersion relations for the heat and charge diffusive modes.

show abstract

Charge diffusion and the butterfly effect in striped holographic matter

Cited by 76 publications

References 93 publications

Diffusion and butterfly velocity at finite density

Diffusion and butterfly velocity at finite density

Holographic butterfly effect at quantum critical points

Diffusion in inhomogeneous media

Contact Info

Product

Resources

About