Related papers: Apparent fractal dimensions in the HMF model
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
In this paper we focus on the finite-dimensional approximation of quasi-static evolutions of critical points of the phase-field model of brittle fracture. In a space discretized setting, we first discuss an alternating minimization scheme…
We show that critical systems of finite size develop a fractal structure in momentum space with anomalous dimension given in terms of the isotherm critical exponent delta of the corresponding infinite system. The associated power laws of…
Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the…
An otherwise free classical particle moving through an extended spatially homogeneous medium with which it may exchange energy and momentum will undergo a frictional drag force in the direction opposite to its velocity with a magnitude…
Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte…
In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and…
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections…
The main purpose of this article is to study box dimension of orbits near hyperbolic and nonhyperbolic fixed points of discrete dynamical systems in higher dimensions. We generalize the known results for one-dimensional systems, that is,…
Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between…
We study random perturbations of Riemannian manifolds $(\mathsf{M},\mathsf{g})$ by means of so-called Fractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields $h^\bullet: \omega\mapsto h^\omega$ will act…
The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies.…
We consider the covariant Lyapunov vectors (CLV) of a high-dimensional Hamiltonian flow in the case of long range potential, namely the Hamiltonian Mean Field (HMF) problem, by studying the behavior of the Lyapunov spectra and the…
We consider the Harper model which describes two dimensional Bloch electrons in a magnetic field. For irrational flux through the unit-cell the corresponding energy spectrum is known to be a Cantor set with multifractal properties. In order…
The relaxation behaviour of isolated quantum systems taken out of equilibrium is among the most intriguing questions in many-body physics. Quantum systems out of equilibrium typically relax to thermal equilibrium states by scrambling local…
Given an arbitrary finite dimensional Hamiltonian H_0, we consider the model H=H_0+\Delta H, where \Delta H is a generic fully connected interaction. By using the strong law of large numbers we easily prove that, for all such models, a…
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…
In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspired by recent results of semiclassical analysis applied to…
The Hamiltonian Mean-Field (HMF) model is a long-range interaction model that exhibits quasi-stationary states associated with a phase transition. Its quasi-stationary states with a lifetime diverging with the number of particles in the…
Mass segregation problem is thought to be entangled with the dynamical evolution of young stellar clusters \cite{olczak}. This is a common sense in the astrophysical community. In this work, the Hamiltonian Mean Field (HMF) model with…