Related papers: Emergence of power-law correlation in 1-dimensiona…
The process of formation of fractal structure in one-dimensional self-gravitating system is examined numerically. It is clarified that structures created in small spatial scale grow up to larger scale through clustering of clusters, and…
Long-time behavior of spatial power-law correlation in one-dimensional self-gravitating system is numerically investigated. It is found that the power-law structure persists even after the system is virialized. The structure gradually…
Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter…
We study the formation of fractal structure in one-dimensional many-body systems with attractive power-law potentials. Numerical analysis shows that the range of the index of the power for which fractal structure emerges is limited.…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also…
We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose…
The self-gravitating systems are formed by particles interacting through gravity. They describe structure formation in the universe. As a consequence of the long range interaction of gravity, they are inhomogeneous even at thermal…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
We study the (newtonian) gravitational force distribution arising from a fractal set of sources. We show that, in the case of real structures in finite samples, an important role is played by morphological properties and finite size…
The nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time. A nontrivial extension of the ordinary quantum mechanics is thus…
Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
First, let the fractal dimension D=n(integer)+d(decimal), so the fractal dimensional matrix was represented by a usual matrix adds a special decimal row (column). We researched that mathematics, for example, the fractal dimensional linear…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
Self-gravitating systems have acquired growing interest in statistical mechanics, due to the peculiarities of the 1/r potential. Indeed, the usual approach of statistical mechanics cannot be applied to a system of many point particles…
Using numerical simulations and scaling theory we study the dynamics of the world-wide Web from the growth rules recently proposed in Ref. [1] with appropriate parameters. We demonstrate that the emergence of power-law behavior of the out-…
We present a model of non-relativistic gravitational theory which is power-counting renormalizable in 3+1 dimensional spacetime. When applied to cosmology, the relativity-violation terms lead to a dark radiation component, which can give…
The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between…
I describe here some features of a non-geometrical approach to quantum gravity which leads to another picture of ties of gravitation and cosmology. The role of taking into account the effect of time dilation of the standard cosmological…