Physics — Open Access Journal

In this work, we investigate a series of mathematical aspects for the fractional diffusion equation with stochastic resetting. The stochastic resetting process in Evans–Majumdar sense has several applications in science, with a particular emphasis on non-equilibrium physics and biological systems. We propose a version of the stochastic resetting theory for systems in which the reset point is in motion, so the walker does not return to the initial position as in the standard model, but returns to a point that moves in space. In addition, we investigate the proposed stochastic resetting model for diffusion with the fractional operator of Prabhakar. The derivative of Prabhakar consists of an integro-differential operator that has a Mittag–Leffler function with three parameters in the integration kernel, so it generalizes a series of fractional operators such as Riemann–Liouville–Caputo. We present how the generalized model of stochastic resetting for fractional diffusion implies a rich class of anomalous diffusive processes, i.e., $⟨{(\Delta x)}^2⟩\propto t^{\alpha }$, which includes sub-super-hyper-diffusive regimes. In the sequence, we generalize these ideas to the fractional Fokker–Planck equation for quadratic potential $U\left(x\right)=a{x}^2+bx+c$. This work aims to present the generalized model of Evans–Majumdar’s theory for stochastic resetting under a new perspective of non-static restart points. Full article

The unitarity condition in the impact parameter space is used to obtain some information about the shape of the interaction region of colliding protons. It is shown that, strictly speaking, a reliable conclusion can be gained only if the behavior of the elastic scattering amplitude (especially, its imaginary part) at all transferred momenta is known. This information is currently impossible to obtain from experimentation. In practice, several assumptions and models are used. They lead to different results as shown below. Full article

The Born postulate can be reduced to its deterministic content that only applies to eigenvectors of observables: The standard probabilistic interpretation of generic states then follows from algebraic properties of repeated measurements and states. Extending this reasoning suggests an interpretation of quantum mechanics generalized with indefinite quantum norm. Full article

We construct a generalized system by introducing an additional long-range hopping to the well-known Su-Schrieffer-Heeger (SSH) model. This system exhibits richer topological properties including non-trivial topological phases and associated localized edge states. We study the zero-energy edge states in detail and derive the edge-state wave functions using two different methods. Furthermore, we propose a possible setup using octupole moments optically excited on an array of dielectric particles for the realization of the system, and by adjusting the coupling strengths between neighboring particles we can control the hotspots (near-field enhancement) in such structures. Full article