Chaos in Yang-Mills matrix models

Başkan, Kağa
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-Shenker-Susskind (BFSS) matrix model. Using an ansatz involving fuzzy-2 and fuzzy-4 sphere configurations we determine reduced effective Hamiltonians through which we study the emerging chaotic dynamics.


Chaos in BFSS and ABJM matrix models
Taşcı, Cankut; Kürkcüoğlu, Seçkin; Yurduşen, İsmet; Department of Physics (2021-7)
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 st...
Covariance Matrix Estimation of Texture Correlated Compound-Gaussian Vectors for Adaptive Radar Detection
Candan, Çağatay; Pascal, Frederic (2022-01-01)
Covariance matrix estimation of compound-Gaussian vectors with texture-correlation (spatial correlation for the adaptive radar detectors) is examined. The texture parameters are treated as hidden random parameters whose statistical description is given by a Markov chain. States of the chain represent the value of texture coefficient and the transition probabilities establish the correlation in the texture sequence. An Expectation-Maximization (EM) method based covariance matrix estimation solution is given ...
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 = ...
Non-Abelian gauge theories of the Yang-Mills type
Abuhatab, Ahmed; Başkal, Sibel; Department of Physics (2003)
In this thesis, starting from the effective Lagrangians of the standard Yang-Mills, higher derivative Yang-Mills and the Chern-Simons- Yang-Mills theories, we have given the corresponding field equations and the symmetric gauge invariant energy- momentum tensors. Lagrangians containing higher derivative terms have been found useful for discussing the long lange effects of the gluon fields. A numeri cal solution is found for a spherically symmetric static gauge potential. On the other hand, Chern-Simons- Yan...
Chaos from equivariant fields on fuzzy S4
Coşkun, Ü. H.; Kürkcüoğlu, Seçkin; Toga, G. C.; Ünal, G. (Springer Science and Business Media LLC, 2018-12)
We examine the 5d Yang-Mills matrix model in 0 + 1-dimensions with U(4N) gauge symmetry and a mass deformation term. We determine the explicit SU(4) ≈ SO(6) equivariant parametrizations of the gauge field and the fluctuations about the classical four concentric fuzzy four sphere configuration and obtain the low energy reduced actions(LEAs) by tracing over the SF 4s for the first five lowest matrix levels. The LEAs so obtained have potentials bounded from below indicating that the equivariant fluctuations ab...
Citation Formats
K. Başkan, “Chaos in Yang-Mills matrix models,” Thesis (M.S.) -- Graduate School of Natural and Applied Sciences. Physics., Middle East Technical University, 2019.