B. Özcan | Searcharxiv

arXiv2026

Real-Time Quantum Dynamics on the Fuzzy Sphere: Chaos and Entanglement

We study the real time quantum dynamics of a matrix model consisting two bosonic fields on the fuzzy sphere using the Gaussian state approximation. Starting from the Hamiltonian formulation and using Wick's theorem, we derive a closed set of coupled nonlinear differential equations governing the time evolution of the one- and two-point correlation functions. Thermal equation of state is found by maximizing the von Neumann entropy over Gaussian states and solving algebraic self-consistency equation(s) leading to a complete determination of the symplectic spectrum of the covariance matrix. We identify near thermal initial conditions and use them to solve the equations of motion and employ our findings to probe chaos by calculating the largest Lyapunov exponent at various temperatures. Our results demonstrate that the latter tends to zero at a finite temperature indicating that the quantum dynamics respect the Maldacena,Shenker,Stanford bound across all temperatures, while approaching toward the classically chaotic regime at high temperatures. Finally, we examine the entanglement dynamics of the model in real-time by considering a sequence of bipartitions of the Hilbert space and computing the entanglement entropy and clearly exhibit the fast scrambling features that emerge in due detail.

hep-th↗

arXiv2023

Non-Abelian Magnetic Field and Curvature Effects on Pair Production

We calculate the Schwinger pair production rates in $\mathbb{R}^{3,1}$ as well as in the positively curved space $S^2 \times \mathbb{R}^{1,1}$ for both spin-$0$ and spin-$\frac{1}{2}$ particles under the influence of an external $SU(2) \times U(1)$ gauge field producing an additional uniform non-abelian magnetic field besides the usual uniform abelian electric field. To this end, we determine and subsequently make use of the spectrum of the gauged Laplace and Dirac operators on both the flat and the curved geometries. We find that there are regimes in which the purely non-abelian and the abelian parts of the gauge field strength have either a counterplaying or reinforcing role, whose overall effect may be to enhance or suppress the pair production rates. Positive curvature tends to enhance the latter for spin-$0$ and suppress it for spin-$\frac{1}{2}$ fields, while the details of the couplings to the purely abelian and the non-abelian parts of the magnetic field, which are extracted from the spectrum of the Laplace and Dirac operators on $S^2$, determine the cumulative effect on the pair production rates. These features are elaborated in detail.

hep-th↗