Related papers: A simple view on the quantum Hall system
We study a fractional quantum Hall system with maximal filling $ \nu = 1/3 $ in the thin torus limit. The corresponding Hamiltonian is a truncated version of Haldane's pseudopotential, which upon a Jordan-Wigner transformation is equivalent…
Account of a system may depend on available methods of gaining information. We discuss a simple discrete system whose description is affected by a specific model of measurement and transformations. It is shown that the limited means of…
This paper investigates quantized thin vortex rings with an internal structure. The quantization scheme of this dynamical system is based on an earlier the approach proposed by the author. Both energy spectrum and circulation spectrum are…
Stacked two dimensional electron systems in transverse magnetic fields exhibit three dimensional fractional quantum Hall phases. We analyze the simplest such phases and find novel bulk properties, e.g., irrational braiding. These phases…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
Quantum considerations have led many theorists to believe that classical black hole physics is modified not just deep inside black holes but at {\it horizon scales}, or even further outward. The near-horizon regime has just begun to be…
We consider spin-polarized electrons in a single Landau level on a torus. The quantum Hall problem is mapped onto a one-dimensional lattice model with lattice constant $2\pi/L_1$, where $L_1$ is a circumference of the torus (in units of the…
The dynamics of relativistic thin shells is a recurrent topic in the literature about the classical theory of gravitating systems and the still ongoing attempts to obtain a coherent description of their quantum behavior. Certainly, a good…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
Getting the mathematical rules for quantised black holes correctly is far from straightforward. Many earlier treatises got it not quite correctly. The general relativistic transformation linking the distant observer (who only detects…
Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. In condensed matter devices, material imperfections hinder a direct…
In classical physics, a single measurement can in principle reveal the state of a system. However, quantum theory permits numerous non-equivalent measurements on a physical system, each providing only limited information about the state.…
We propose a unitary matrix Chern-Simons model representing fractional quantum Hall fluids of finite extent on the cylinder. A mapping between the states of the two systems is established. Standard properties of Laughlin theory, such as the…
The ground states of electrons in two vertically coupled quantum dots in the presence of an external magnetic field have been studied within the density functional theory. A phase diagram of the transition to the quantum Hall state in…
The coherent states for the quantum mechanics on a torus and their basic properties are discussed.
Transport properties of bilayer quantum Hall systems at $\nu=1/q$, where $q$ is an odd integer, are investigated. The edge theory is used for the investigation, since tunneling between the two layers is assumed to occur on the edge of the…
We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…
In the model where the Universe is considered as a thin shell expanding in 5-dimensional hyper-space there is a possibility to have just one scale for a particle theory corresponding to the Universe thickness. From a realistic model the…
The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may…
Strong driving of quantum systems opens opportunities for both controlling and characterizing their states. For theoretical studying of these systems properties we use the rate-equation formalism. The advantage of such approach is its…