SYK model, chaos and conserved charge

This note is devoted to the investigation of Susskind's proposal [1] concerning the correspondence between the operator growth in chaotic theories and the radial momenta of the particle falling in the AdS black hole. We study this proposal and consider the simple example of an operator with the global charge described by the charged particle falling to the Reissner-Nordstrom-AdS black hole. Different charges of the particle lead to qualitatively different behavior of the particle momenta and consequently change of the operator size behavior. This holographic result is supported by different examples of chaotic models with a finite chemical potential where the suppression of chaos has been observed.

Section: Discussion and Connection With Syk-like Modelsmentioning

confidence: 55%

“…In [6] it was shown, that in the SYK model with the complex fermions introduction of the chemical potential lead to the effect of chaos damping. There is a little difference with our results.…”

Section: Discussion and Connection With Syk-like Modelsmentioning

confidence: 99%

When things stop falling, chaos is suppressed

Ageev

Aref’eva

2019

“…are associated with x ± respectively. of a chemical potential [21]. Here the Lypunov index computed was found to be bounded by 2π/β.…”

Section: Resultsmentioning

confidence: 81%

BTZ dynamics and chaos

Poojary

2020

We find an effective action for gravitational interactions with scalars in AdS 3 to first order in G N at the conformal boundary. This action can be understood as an action for the Brown-Henneaux modes and is given by the square-root product of right and left moving Schwarzian derivatives for conformal transformations of the boundary. We thus reproduce the result λ L = 2π β for OTOC computed first in arXiv:1412.6087 for a Schwarzchild black hole in AdS 3 . Applying the same procedure to rotating BTZ we find the Lyapunov index to be λ L = 2π β + > 2π β where β + = β(1 − µ L ), with µ L = r − r + being the chemical potential for angular momentum. We thus comment on a possible modification to a part of the proof given in arXiv:1503.01409 to accommodate this result.

“…Indeed, some studies addressing the connection between the RMT properties of SYK and the OTOCs appeared in recent days: very recently, [58] has studied the onset of RMT behavior in the (Gaussian filtered) SYK SFF 6 and found that, in agreement with the results of [59], the time-scale at which the RMT behavior appears -which we will call Thouless time -is not the 4 Indeed, a priori there could be systems which are chaotic according to one definition and not chaotic according to the other. 5 For example, see the U (1) symmetry and flavor generalizations [16][17][18][19][20][21], supersymmetric generalizations [22][23][24][25][26][27], SYK(-like) models without disorder [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], gravity duals [44][45][46][47][48][49][50][51] and the Schwarzian theory [52][53][54]. 6 As we will revi...…”

Section: Introductionmentioning

confidence: 99%

The Thouless time for mass-deformed SYK

Nosaka¹,

Rosa²,

Yoon³

2018

We study the onset of RMT dynamics in the mass-deformed SYK model (i.e., an SYK model deformed by a quadratic random interaction) in terms of the strength of the quadratic deformation. We use as chaos probes both the connected unfolded Spectral Form Factor (SFF) as well as the Gaussian-filtered SFF, which has been recently introduced in the literature. We show that they detect the chaotic/integrable transition of the massdeformed SYK model at different values of the mass deformation: the Gaussian-filtered SFF sees the transition for large values of the mass deformation; the connected unfolded SFF sees the transition at small values. The latter is in qualitative agreement with the transition as seen by the OTOCs. We argue that the chaotic/integrable deformation affect the energy levels inhomogeneously: for small values of the mass deformation only the lowlying states are modified while for large values of the mass deformation also the states in the bulk of the spectrum move to the integrable behavior. * nosaka@yukawa.kyoto-u.ac.jp † Dario85@kias.re.kr ‡ junggi.yoon@icts.res.in arXiv:1804.09934v1 [hep-th]