Related papers: Fractons and Fractal Statistics
We consider the concept of fractons in the context of high-$T_{c}$ superconductivity. These objects, which carry rational or irrational quantum numbers, are classified into universal classes $h$ of particles or quasiparticles which obey…
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest…
Anyons occur in two-dimensional electron systems as excitations with fractional charge in the topologically ordered states of the Fractional Quantum Hall Effect (FQHE). Their dynamics are of utmost importance for topological quantum phases…
We construct first a class of Moran fractals in R^d with countably many generators and non-stationary contraction rates; at each step n, the contractions depend on n-truncated sequences, and are related to asymptotic letter frequencies. In…
A many-particle Hamiltonian is proposed in order to explain the fractional quantum Hall effect (FQHE) for fractional filling factors $\nu < 1$. The solutions of the corresponding Hartree-Fock equations make it possible to discuss the FQHE…
One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clear reflected in this kind…
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a…
We review what is known about fracton phases of quantum matter. Fracton phases are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics, or mobile only in certain directions.…
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…
Hausdorff dimensions of level sets of generic continuous functions defined on fractals were considered in two papers by R. Balka, Z. Buczolich and M. Elekes. In those papers the topological Hausdorff dimension of fractals was defined. In…
This is an introduction to the microscopic theories of the FQHE. After a brief description of experiments, trial wavefunctions and the physics they contain are discussed. This is followed by a description of the hamiltonian approach,…
We give a simple macroscopic phase-space explanation of fractional quantum Hall effect (FQHE), in a fashion reminiscent of the Landau-Ginsburg macroscopic symmetry breaking analyses. This is in contrast to the more complicated microscopic…
Anyon usually exists as collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. Fractional quantum Hall effect (FQHE)…
The braid group dynamics captures the fractional quantum Hall effect (FQHE) as a manifestation of puncture phase. When the dynamics is generalized for particles on a multi-sheeted surface, we obtain new tools which determine the fractional…
The notion of fractality, in the context of positive-valued probability distributions, is conventionally associated with the class of Paretian probability laws. In this research we show that the Paretian class is merely one out of six…
A quantum statistical theory is developed for a fractional quantum Hall effects in terms of composite bosons (fermions) each of which contains a conduction electron and an odd (even) number of fluxons. The cause of the QHE is by assumption…
We present a drop model for integer and fractional quantum Hall effects (FQHE). We show that the two-dimensional electron gas breaks up into regions with filling factors {\nu} = 1 and {\nu} = 0 in disk geometry, and the formation of drops…
A large class of fractional quantum Hall (FQH) states can be classified according to their pattern of zeros, which describes the way ideal ground state wave functions go to zero as various clusters of electrons are brought together. In this…
The observation of the fractional quantum Hall (FQH) effect in 2D electron gases ushered in investigations of topological phases driven by strong electron correlations. Their remarkable features include fractionalized elementary…
We review a burgeoning field of "fractons" -- a class of models where quasi-particles are strictly immobile or display restricted mobility that can be understood through generalized multipolar symmetries and associated conservation laws.…