We develop a hybrid classical–quantum method for solving the Lorenz system. We use the forward Euler method to discretize the system in time, transforming it into a system of equations. This set of equations is solved by using the Variational Quantum Linear Solver (VQLS) algorithm. We present numerical results comparing the hybrid method with the classical approach for solving the Lorenz system. The simulation results demonstrate that the VQLS method can effectively compute solutions comparable to classical methods. The method is easily extended to solving similar nonlinear differential equations.

In this article, we investigate the interactions of a Yang-Mills (YM) wave fluctuation of a classical isotropic, homogeneous YM condensate, which models gluon plasma, with a gravitational wave (GW). We re-analyse the study of fluctuations of the gluon plasma using vector decomposition of the gauge field into scalar, longitudinal, and transverse modes. We find that there is an energy transfer between isotropic gluon condensate and plasmon modes, but the effect is delayed due to GW, and dependent on the initial conditions. We also study quarks in the background of YM condensate and GW. We find that the quarks break the isotropy of the condensate and the GW couples quarks of different flavours of the SU(2) group. Thus, the GW induces flavour fluctuations, which has interesting implications for experimental observations and quark-gluon plasma physics.

In this paper, we discuss the interaction of non-Abelian SU(2) Yang-Mills progressive waves with gravitational waves. We solve and obtain some interesting solutions to pure Yang-Mills equations in different backgrounds, and perturbative solutions induced due to gravitational waves. These perturbations show `beat patterns' and depending on boundary conditions, changes in frequency. In flat space-time, when the Yang-Mills fields and the gravitational waves are in the same direction there is no interaction, unless there is self interaction of the Yang-Mills fields. In the system with non-zero self interaction the amplitudes of the perturbation are inversely proportional to the Yang-Mills coupling constant. In a cosmological background, the Yang-Mills fields and the gravitational wave interact when they are in the same direction even without self interaction of the Yang-Mills progressive fields. We find that in the electroweak symmetry broken phase of the gauge fields, the interactions are perturbative only for an infinitesimal time.

Quark-Gluon Plasma (QGP), a strongly interacting state of the early universe, exhibits remarkably fluid-like behavior despite its underlying non-Abelian dynamics. Motivated by these features, we explore time-dependent SU(2) Yang-Mills condensates as non-linear classical background fields to model QGP. We first study quarks in gluon backgrounds and show that quark back-reaction can break the isotropy of the condensate for certain initial conditions. We then compute the one-loop finite-temperature effective action using the background-field method and heat-kernel expansion. The resulting thermodynamic pressure increases with temperature but exhibits an approximately logarithmic dependence. This is expected, as this is the de-confined phase of QGP; it is not exactly an ideal gas due to self-interaction. We also perform lattice calculations for the system to contrast continuum and lattice perspectives. We then add the GW to the thermodynamic QGP model and show that certain frequencies of the GW can induce instabilities in the QGP. Our analysis explores the limitations and role of non-perturbative, time-dependent backgrounds in semi-classical description of Yang-Mills dynamics.