Narrow Results

The mixed phase space in an open quantum dot array with a soft confining potential is studied in low and high magnetic fields. Chaos occurs due to the perturbations by the constrictions connecting the dots of the array. Regular orbits and the areas of Kalmogorov-Arnold-Moser islands in phase space become increasingly dominating with increasing magnetic field. The correspondence to the high-field quantum-mechanical picture in a 2D electron system with boundaries is discussed.

This paper is devoted to studying the phase space portrait of FRW universe by taking different linear forms of coupling between scalar field models and dark matter with nonlinear electromagnetic effects. We introduce normalized dimensionless quantities to construct an autonomous system of equations. We evaluate critical points and respective eigenvalues for different parameters to analyze the stability of the cosmos. These points show saddle/unstable behavior for tachyon coupled field with the nonaccelerating universe. In the case of phantom energy, the stability decreases for some critical points which also represent the nonaccelerating universe. We conclude that the dynamical stability of the isotropic and homogeneous universe model reduces in the presence of nonlinear electrodynamics for tachyon as well as the phantom field.

This paper is devoted to analyze the stability of locally rotationally symmetric Bianchi type I model through phase space portrait in the presence of nonlinear electrodynamics. The normalized dimensionless quantities are introduced to construct an autonomous system of equations. The critical points and respective eigenvalues are evaluated for different linear forms of coupling between scalar field models and dark matter to discuss the stability of the cosmos. We conclude that the increase/decrease of stability in the presence of nonlinear electrodynamics completely depends on the choice of interaction terms between matter and dark energy models.

We examine the cosmic scenario of interacting Kaniadakis holographic dark energy in dynamical Chern–Simons modified gravity and the fractal universe. For this purpose, the Hubble, deceleration, coincidence, equation-of-state and jerk parameters have been evaluated in view of the redshift parameter. It is observed that deceleration parameter $(q)$ evaluates the accelerated expansion of the universe in both gravities. The coincidence parameter $(u)$ exhibits the transition of behavior from dark matter to dark energy era of the universe. The behavior of the equation-of-state parameter $({\omega }_{\theta })$ describes the quintessence and vacuum regions of the universe in both gravities for maximum choices of the interacting parameters. The jerk parameter shows the correspondence of the given model with $\mathrm{\Lambda }$CDM model and other standard models in both gravities. All the parameters exhibit consistent behavior with the Planck 2018 data. We also analyze the dynamical stability in both frameworks by formulating dynamical models in the form of a system of differential equations and evaluating their corresponding critical points. Critical points of both models are stable and phase plots indicate attractor behavior that implies stability of the models. Further, stability conditions of both models signify the accelerating expansion of the universe. In addition, we discuss the thermodynamics of this model with the generalized second law and find its validity in both frameworks.