Abstract:
This thesis consists of three parts. In first, we will examine the validity of the geodesic
rule, a key postulate of the Kibble-Zurek mechanism, which describes topological defect
formation during second-order phase transitions. Using equilibrium Monte Carlo simulations of the XY model and a complex scalar field theory, we find that thermal fluctuations
cause a breakdown of the geodesic rule, leading to a higher defect density than standard
predictions.
The second part explores how spacetime oscillations affect fluctuations in non-Abelian
SU(2) gauge fields. Oscillatory terms in the metric enter the evolution equations, generating resonance in field fluctuations. Initially, when fluctuations are small and terms
nonlinear in gauge fields can be ignored, the dynamics similar to U(1) gauge fields. In
this linear regime, field modes exhibit parametric resonance. However, as non-Abelian
effects emerge, SU(2) gauge fields show enhanced growth, leading to increased energy
density and tr(FF˜).
Finally, we will discuss Z3 symmetry in 2+1 flavor QCD. The presence of dynamical
fermions break the Z3 symmetry explicitly. Consequently, in the deconfined phase two
meta-stable states appear for high enough temperatures. Our preliminary results suggest
that these states may be present for temperatures(370MeV< Tm ≤ 446MeV) achieved in
Heavy-ion collision experiments
