Chaos in BFSS and ABJM matrix models

Taşcı, Cankut
In this thesis, we focus on the chaotic dynamics emerging from Banks-Fischler- Shenker-Susskind (BFSS) and Aharony-Bergman-Jafferis-Maldacena (ABJM) models. We first direct our attention on the bosonic part of the BFSS model and introduce mass deformation terms. Using ansatz configurations involving fuzzy-2 and fuzzy-4 spheres with collective time dependence, we find a family of reduced effective Hamiltonians through which we explore the chaotic dynamics emerging from these models. In order to reveal the structure of the chaotic dynamics, we calculate the Lyapunov exponents and plot the Poincaré sections at several different values of the parameters of the system. Secondly, we focus on the bosonic part of the mass deformed ABJM model and obtain a matrix model by reducing it from 2+1 to 0+1 dimensions. Using ansatz configurations consisting of Gomis, Rodriguez-Gomez, Van Raamsdonk and Verlinde (GRVV) matrices, which also describe fuzzy-2 spheres with collective time dependence, we obtain reduced effective Hamiltonians and explore their chaotic dynamics. Relation of our results to the Maldacena-Shenker-Stanford (MSS) bound λ ≤ 2ℼT and the largest Lyapunov exponent is also discussed in detail in both cases.


Chaos in Yang-Mills matrix models
Başkan, Kağa; Kürkcüoğlu, Seçkin; Department of Physics (2019)
In this thesis, chaotic dynamics emerging from Yang-Mills matrix models are investigated. Firstly, we investigate the Yang-Mills two-matrix models with ChernSimons term using both analytical and numerical methods. In particular, we obtain the Poincaré sections and Lyapunov exponents at several different values of the parameters of the model, revealing the detailed structure of the chaotic dynamics. In the second part of the thesis, we focus on a massive deformation of the bosonic part of the Banks-Fischler-...
Dynamics for chaos and fractals
Alejaily, Ejaily; Akhmet, Marat; Department of Mathematics (2019)
In this thesis, we study how to construct and analyze dynamics for chaos and fractals. After the introductory chapter, we discuss in the second chapter the chaotic behavior of hydrosphere parameters and their influence on global weather and climate. For this purpose, we investigate the nature and source of unpredictability in the dynamics of sea surface temperature. The impact of sea surface temperature variability on the global climate is clear during some global climate patterns like the El Niño-Southern ...
Chaos in economic models with exogenous shocks
Akhmet, Marat; Fen, Mehmet Onur (Elsevier BV, 2014-10-01)
We investigate the generation of chaos in economic models through exogenous shocks. The perturbation is formulated as a pulse function where either values or instants of discontinuity are chaotically behaved. We provide a rigorous proof of the existence of chaos in the perturbed model. The analytical results are applied to Kaldor-Kalecki-type models of the aggregate economy subject to export and rainfall shocks, respectively. Simulations are used to demonstrate the emergence and the control of chaos. Our re...
Chaos from massive deformations of Yang-Mills matrix models
Başkan, K.; Kürkcüoğlu, Seçkin; Oktay, O.; Taşcı, Cankut (Springer Science and Business Media LLC, 2020-10-01)
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) x SO(3) x 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 = ...
Chaos in the SU (2) Yang-Mills Chern-Simons matrix model
Başkan, Kağan; Kürkcüoğlu, Seçkin (2021-09-15)
We study the effects of addition of the Chern-Simons (CS) term in the minimal Yang-Mills (YM) matrix model composed of two 2×2 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, pφ, associated to the SO(2) symmetry. We examine the behavior of the emerging chaotic dynamics by computing the Lyapunov exponents and pl...
Citation Formats
C. Taşcı, “Chaos in BFSS and ABJM matrix models,” M.S. - Master of Science, Middle East Technical University, 2021.