Related papers: Wavelet-based multiresolution analysis of quantum …
Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
We report a clear evidence of atomic fractals in the nonlinear motion of a two-level atom in a standing-wave microcavity. Fractal-like structures, typical for chaotic scattering, are numerically found in the dependencies of outgoing…
We consider the influence of the Fermi statistics of nucleons on the binding energy of a new type of nuclear structures such as fractal nuclear clusters (fractal isomers of nuclei). It is shown that the fractal nuclear isomers possess a…
We numerically analyse quantum survival probability fluctuations in an open, classically chaotic system. In a quasi-classical regime, and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal…
Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling…
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together…
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…
The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions…
We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in…
Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…
Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a…
Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based. Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of…
Inspired by various quantum gravity approaches, we explore quantum field theory where spacetime exhibits scaling properties and dimensional reduction with changing energy scales, effectively behaving as a multifractal manifold. Working…
A field theory is presented for predicting damage and fracture in quasi-brittle materials. The approach taken here is new and blends a non-local constitutive law with a two-point phase field. In this formulation, the material displacement…