Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
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Springer
Received: July 29, Revised: August 31, Accepted: September 8, Published: October 13,
2020 2020 2020 2020
Navid Abbasia and Sara Taheryb a
School of Nuclear Science and Technology, Lanzhou University, 222 South Tianshui Road, Lanzhou 730000, China b Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
E-mail: [email protected], [email protected] Abstract: We develop a method to study coupled dynamics of gauge-invariant variables, constructed out of metric and gauge field fluctuations on the background of a AdS 5 Reissner-Nordstr¨ om black brane. Using this method, we compute the numerical spectrum of quasinormal modes associated with fluctuations of spin 0, 1 and 2, non-perturbatively in µ/T . We also analytically compute the spectrum of hydrodynamic excitations in the small chemical potential limit. Then, by studying the spectral curve at complex momenta in every spin channel, we numerically find points at which hydrodynamic and non-hydrodynamic poles collide. We discuss the relation between such collision points and the convergence radius of the hydrodynamic derivative expansion. Specifically in the spin 0 channel, we find that within the range 1.1 . µ/T . 2, the radius of convergence of the hydrodynamic sound mode is set by the absolute value of the complex momentum corresponding to the point at which the sound pole collides with the hydrodynamic diffusion pole. It shows that in holographic systems at finite chemical potential, the convergence of the hydrodynamic derivative expansion in the mentioned range is fully controlled by hydrodynamic information. As the last result, we explicitly show that the relevant information about quantum chaos in our system can be extracted from the pole-skipping points of energy density response function. We find a threshold value for µ/T , lower than which the pole-skipping points can be computed perturbatively in a derivative expansion. Keywords: Gauge-gravity correspondence, AdS-CFT Correspondence ArXiv ePrint: 2007.10024
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)076
JHEP10(2020)076
Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
Contents 1 Introduction
2
2 Gauge invariant variables
6
3 Quasinormal modes from coupled differential equations
8
5 Complex life of quasinormal modes and the radius of convergence of the hydrodynamic derivative expansion 5.1 Spin 0 channel 5.2 Spin 1 channel 5.3 Comment about the radius of convergence in the spin 0 channel and review of the results
22 23 28 30
6 Quasinormal modes and the chaos point 6.1 Chaos point from shock wave computations 6.2 Pole-skipping
32 33 34
7 Review, conclusion and outlook
38
A Diffeomorphism and gauge transformations
40
B Frobenius solution
40
C Near-boundary behavior of gauge invariant quantities
41
D Comparing between the method developed in section 3 and that of Kaminski et al. [43] 42 E Numerical values of quasinormal modes associated with spin
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