Phase diagram of QCD chaos in linear sigma models and holography

Self Cite

We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.

“…This was a motivation for the model of[18], and string theory matrix models in similar spirit are found in[47][48][49][50] 4. For related chaos analyses, see[52][53][54] 5.…”

mentioning

confidence: 76%

Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Hashimoto

Huh

Kim

et al. 2020

Self Cite

“…For example, in the Sachdev-Ye-Kitaev (SYK) model, it was confirmed that the bound is saturated. The Lyapunov exponent in gravity systems has been extensively studied (and also [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]). For a test particle, the Lyapunov exponents in static and spherically symmetric spacetimes [17,19,23,27,28,38,39,41], rotating black hole spacetimes [13,19,24,30], the magnetized Ernst-Schwarzschild spacetime [18], multi-black hole spacetimes [20], the Myers-Perry black hole spacetime [26,41], the Einstein-Maxwell-dilaton gravity [32,39], and a black hole with quasi-topological electromagnetism [40] have been evaluated.…”

Section: Introductionmentioning

confidence: 99%

Violation of bound on chaos for charged probe in Kerr-Newman-AdS black hole

Gwak

Kan

Lee

et al. 2022

We investigate the conjectured bound on the Lyapunov exponent for a charged particle with angular motion in the Kerr-Newman-AdS black hole. The Lyapunov exponent is calculated based on the effective Lagrangian. We show that the negative cosmological constant reduces the chaotic behavior of the particle, namely, it decreases the Lyapunov exponent. Hence, the bound is more effective in the AdS spacetime than in the flat spacetime. Nevertheless, we find that the bound can be violated when the angular momenta of the black hole are turned on. Moreover, we show that in an extremal black hole, the bound is more easily violated compared to that in a nonextremal black hole.

“…For example, a possible explanation of quantum chaos in the hadronic spectrum by a holographic approach can be found in [14]. Probing the phase diagram of QCD chaos is a challenging task, an option effectively explored in [15].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic and frame dependent chaos of suspended strings from a dynamical holographic QCD model with magnetic field

Shukla

Dudal

Mahapatra

2023

We investigate both from a qualitative as well as quantitative perspective the emergence of chaos in the QCD confining string in a magnetic field from a holographic view-point. We use an earlier developed bottom-up solution of the Einstein-Maxwell-Dilaton action that mimics QCD and its thermodynamics quite well. Surprisingly, our predictions depend on the used frame: the magnetic field tends to suppress the chaos in both perpendicular and parallel directions relative to the magnetic field in the string frame whilst in the Einstein frame, the chaos suppression only happens in the perpendicular direction, with an enhanced chaos along the magnetic field. The amount of suppression/enhancement in both frames does depend on the relative orientation of the string and magnetic field.