arXiv subjects

K. Başkan

Publications and source records attributed to K. Başkan.

4 recordsLinked to original sources

arXiv2023

Chaotic Dynamics of the Mass Deformed ABJM Model

We explore the chaotic dynamics of the mass-deformed Aharony-Bergman-Jafferis-Maldacena model. To do so, we first perform a dimensional reduction of this model from $2+1$ to $0+1$ dimensions, considering that the fields are spatially uniform. Working in the 't Hooft limit and tracing over ansatz configurations involving fuzzy 2-spheres, which are described in terms of the Gomis-Rodriguez-Gomez-Van Raamsdonk-Verlinde matrices with collective time dependence, we obtain a family of reduced effective Lagrangians and demonstrate that they have chaotic dynamics by computing the associated Lyapunov exponents. In particular, we focus on how the largest Lyapunov exponent, $λ_L$, changes as a function of $E/N^2$. Depending on the structure of the effective potentials, we find either $λ_L \propto (E/N^2)^{1/3}$ or $λ_L \propto (E/N^2 - γ_N)^{1/3}$, where $γ_N(k, μ)$ are constants determined in terms of the Chern-Simons coupling $k$, the mass $μ$, and the matrix level $N$. Noting that the classical dynamics approximates the quantum theory only in the high-temperature regime, we investigate the temperature dependence of the largest Lyapunov exponents and give upper bounds on the temperature above which $λ_L$ values comply with the Maldacena-Shenker-Stanford bound, $ λ_L \leq 2 πT $, and below which it will eventually be not obeyed.

hep-th↗

arXiv2022

Chaos in Matrix Gauge Theories with Massive Deformations

Starting from an $SU(N)$ matrix quantum mechanics model with massive deformation terms and by introducing an ansatz configuration involving fuzzy four- and two-spheres with collective time dependence, we obtain a family of effective Hamiltonians, $H_n \,, (N = \frac{1}{6}(n+1)(n+2)(n+3))$ and examine their emerging chaotic dynamics. Through numerical work, we model the variation of the largest Lyapunov exponents as a function of the energy and find that they vary either as $\propto (E-(E_n)_F)^{1/4} $ or $\propto E^{1/4}$, where $(E_n)_F$ stand for the energies of the unstable fixed points of the phase space. We use our results to put upper bounds on the temperature above which the Lyapunov exponents comply with the Maldacena-Shenker-Stanford (MSS) bound, $2 πT $, and below which it will eventually be violated.

hep-th↗

arXiv2021

Chaos in $SU(2)$ Yang-Mills Chern-Simons Matrix Model

We study the effects of addition of Chern-Simons (CS) term in the minimal Yang Mills (YM) matrix model composed of two $2 \times 2$ matrices with $SU(2)$ gauge and $SO(2)$ global symmetry. We obtain the Hamiltonian of this system in appropriate coordinates and demonstrate that its dynamics is sensitive to the values of both the CS coupling, $κ$, and the conserved conjugate momentum, $p_ϕ$, associated to the $SO(2)$ symmetry. We examine the behavior of the emerging chaotic dynamics by computing the Lyapunov exponents and plotting the Poincaré sections as these two parameters are varied and, in particular, find that the largest Lyapunov exponents evaluated within a range of values of $κ$ are above that is computed at $κ=0$, for $κp_ϕ< 0$. We also give estimates of the critical exponents for the Lyapunov exponent as the system transits from the chatoic to non-chaotic phase with $p_ϕ$ approaching to a critical value.

hep-th↗

arXiv2020

Chaos from Massive Deformations of Yang-Mills Matrix Models

We focus on an $SU(N)$ Yang-Mills gauge theory in $0+1$-dimensions with the same matrix content as the bosonic part of the BFSS matrix model, but with mass deformation terms breaking the global $SO(9)$ symmetry of the latter to $SO(5) \times SO(3) \times {\mathbb Z}_2$. Introducing an ansatz configuration involving fuzzy four and two spheres with collective time dependence, we examine the chaotic dynamics in a family of effective Lagrangians obtained by tracing over the aforementioned ansatz configurations at the matrix levels $N = \frac{1}{6}(n+1)(n+2)(n+3)$, for $n=1,2,\cdots\,,7$. Through numerical work, we determine the Lyapunov spectrum and analyze how the largest Lyapunov exponents(LLE) change as a function of the energy, and discuss how our results can be used to model the temperature dependence of the LLEs and put upper bounds on the temperature above which LLE values comply with the Maldacena-Shenker-Stanford (MSS) bound $2 πT $ , and below which it will eventually be violated.

hep-th↗