相关论文: Time Evolution of Quantum Fractals
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
We analyze the time evolution of a one-dimensional quantum system with zero range potential under time periodic parametric perturbation of arbitrary strength and frequency. We show that the projection of the wave function on the bound state…
The interplay between thermodynamics, general relativity and quantum mechanics has long intrigued researchers. Recently, important advances have been obtained in thermodynamics, mainly regarding its application to the quantum domain through…
Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship is given between the…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
In this work, I review some aspects concerning the evolution of quantum low-energy fields in a foamlike spacetime, with involved topology at the Planck scale but with a smooth metric structure at large length scales, as follows. Quantum…
We explicitly construct fractals of dimension 4-epsilon on which dimensional regularization approximates scalar-field-only quantum-field-theory amplitudes. The construction does not require fractals to be Lorentz-invariant in any sense, and…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
A profound quantum-gravitational effect of space-time dimension running with respect to the size of space-time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of…
We review recent developments in the understanding of the fractal properties of quantum spacetime of 2d gravity coupled to c>0 conformal matter. In particular we discuss bounds put by numerical simulations using dynamical triangulations on…
We investigate the evolution of matter density perturbations within a fractional cosmological framework inspired by fractal space-time constructions in field theory, where a deformation of the integration measure induces non-locality and…
Wavepackets in quantum mechanics spread and the Universe in cosmology expands. We discuss a formalism where the two effects can be unified. The basic assumption is that the Universe is determined by a unitarily evolving wavepacket defined…
We analyze the size and evolution of quantum fluctuations of cosmologically relevant geometric observables, in the context of the effective relational cosmological dynamics of GFT models of quantum gravity. We consider the fluctuations of…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
We employ Riesz's fractional derivative into the Wheeler--DeWitt equation for a closed de Sitter geometry and obtain the no-boundary and tunneling wavefunctions. From the corresponding probability distributions, the event horizon of the…
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
The phenomenological universalities (PU) are extended to include time-depended quantum oscillatory phenomena, coherence and supersymmetry. It will be proved that this approach generates minimum uncertainty coherent states of time-dependent…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…