Related papers: Bounding multifractality by observables
The similarity in fractal dimensions of paint ``blobs'' in samples of gestural expressionist art implies that these pigment structures are statistically indistinguishable from one another. This result suggests that such dimensions cannot be…
Spectroscopic measurements in quantum systems are subject to selection rules, usually based on space-time symmetries, that allow or disallow transitions between states. In many-body systems, in addition to the single-particle states, there…
The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as…
The Aubry-Andre model is a one-dimensional lattice model for quasicrystals with localized and delocalized phases. At the localization transition point, the system displays fractal spectrum, which relates to the Hofstadter butterfly. In this…
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension.…
By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction…
Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized correlation dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy…
Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing…
We study many-body localization in a hardcore boson model in the presence of random disorder on finite generation fractal lattices with different Hausdorff dimensions and different local lattice structures. In particular, we consider the…
Algorithmic fractal dimensions -- constructs of computability theory -- have recently been used to answer open questions in classical geometric measure theory, questions of mathematical analysis whose statements do not involve computability…
We propose a new quantity called modulus fidelity to measure the closeness of two quantum pure states. Especially, we use it to investigate the closeness of eigenstates of quantum many-body systems. When the system is integrable, the…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
Following \cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimension of sets which can be defined in a recursive way and we…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
Understanding the stability of integrability in many-body quantum systems is key to controlling dynamics and predicting thermalization. While the breakdown of integrability in short-range interacting systems is well understood, the role of…
We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or…
Fractal structures are observed in the universe in two very different ways. Firstly, in the gas forming the cold interstellar medium in scales from 10^{-4} pc till 100 pc. Secondly, the galaxy distribution has been observed to be fractal in…
Ergodicity in quantum many-body systems is - despite its fundamental importance - still an open problem. Many-body localization provides a general framework for quantum ergodicity, and may therefore offer important insights. However, the…