Phase space analysis of interacting and non-interacting models in f(Q,C)gravity

Using a dynamical system method,we study a Friedmann-Robertson-Walker(FRW)cosmological model within the context of f(Q,C)gravity,where Q is the non-metricity scalar and C represents the boundary term,considering both interacting and non-interacting models.A set of autonomous equations is derived,and solutions are calculated accordingly.We assess the critical points obtained from these equations,identify their characteristic values,and explore the physical interpretation of the phase space for this system.Two types of f(Q,C)are assumed:(i)f(Q,C)=Q+αQ+βClogC and(i)f(Q,C)=Q+αQ+β/C,where α and β are the parameters.In Model I,we obtain two stable critical points,whereas in Model Il,we identify three stable critical points for both interacting and non-interacting models.We examine the behavior of phase space trajectories at every critical point.We calculate the values of the physical parameters for both systems at each critical point,indicating the accelerated expansion of the Universe.

Phase Space Analysis and Anisotropic Universe Model in f(T) Gravity

In this paper, we study the stability of locally rotationally symmetric （LRS） Bianchi I universe model in f（T） gravity through phase space analysis. We assume that the f（T） gravity can be treated as effective dark energy behaving like perfect fluid, and suggest that there are interactions between pressureless matter as well as dark energy. We construct the corresponding autonomous system of equations to check the stability of the model for non phantom, vacuum and phantom phases. It is concluded that critical points remain more stable in phantom phase as compared to non phantom and vacuum cases. Finaily, we discuss the cosmological behavior of the model through some cosmological parameters.

The dynamical properties of a Rydberg hydrogen atom between two parallel metal surfaces

This paper presents the dynamical properties of a Rydberg hydrogen atom between two metal surfaces using phase space analysis methods. The dynamical behaviour of the excited hydrogen atom depends sensitively on the atom-surface distance d. There exists a critical atom-surface distance dc = 1586 a.u. When the atom-surface distance d is larger than the critical distance de, the image charge potential is less important than the Coulomb potential, the system is near-integrable and the electron motion is regular. As the distance d decreases, the system will tend to be non-integrable and unstable, and the electron might be captured by the metal surfaces.