Related papers: Some Basic Aspects of Fractional Quantum Numbers
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
We present here a complete microscopic theory of a family of neutral excitations in the fractional quantum Hall fluids, related to the geometric fluctuations of the quantum Hall ground states. Many of the physical properties of such…
The quest for universal signatures of topological phases is fundamentally important since these properties are robust to variations in system-specific details. Here we present general results for the response of quantum Hall states to…
Based on the requirement of covariance, we propose a new approach for generalizing fractional calculus in multi-dimensional space. As a first application we calculate an approximation for the ground state energy of the fractional…
The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of…
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum…
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
As a model for the transitions between plateaus in the fractional Quantum Hall effect we study the critical behavior of non-interacting charged particles in a static random magnetic field with finite mean value. We argue that this model…
Using a well known singular gauge transformation, certain fractional quantized Hall states can be modeled as integer quantized Hall states of transformed fermions interacting with a Chern-Simons field. In previous work we have calculated…
In order to obtain a local description of the short distance physics of fractionally quantized Hall states for realistic (e.g. Coulomb) interactions, I propose to view the zeros of the ground state wave function, as seen by an individual…
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 an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…
Some purely chiral fractional quantum Hall states are described by symmetric or anti-symmetric polynomials of infinite variables. In this article, we review a systematic construction and classification of those fractional quantum Hall…
This review presents experimental results on the inter-edge-state transport in the quantum Hall effect, mostly obtained in the regime of high imbalance. The application of a special geometry makes it possible to perform I-V spectroscopy…
A simple algebraic model for charged particle moving in two dimensional space under influence of singular magnetic field is given. The fundamental assumption for the model is that every charged particle coupled to the magnetic field is…
The composite Fermion (CF) picture offers a simple intuitive way of understanding many of the surprising properties of a strongly interacting two-dimensional electron fluid in a large magnetic field. The simple way in which the mean field…
We compare quantum Hall systems at filling factor 2 to those at filling factors 2/3 and 2/5, corresponding to the exact filling of two lowest electron or composite fermion (CF) Landau levels. The two fractional states are examples of CF…
We consider the quantum Hall effect (QHE) in a system of interacting electrons. Our formalism is valid for systems in the presence of an external magnetic field, as well as for systems with a nontrivial band topology. That is, the…