Related papers: On the relation between the anyon and Calogero mod…
We examine the anyon representation of the Laughlin quasi-holes, in particular the one-dimensional, algebraic aspects of the representation. For the cases of one and two quasi-holes an explicit mapping to anyon systems is given, and the…
We study the magnetic properties of electron in a constant magnetic field and confined by a isotropic two dimensional harmonic oscillator on a space where the coordinates and momenta operators obey generalized commutation relations leading…
We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1,…
The statistical mechanics of an anyon gas in a magnetic field is addressed. An harmonic regulator is used to define a proper thermodynamic limit. When the magnetic field is sufficiently strong, only exact $N$-anyon groundstates, where…
Two-dimensional tight-binding models for quasicrystals made of plaquettes with commensurate areas are considered. Their energy spectrum is computed as a function of an applied perpendicular magnetic field. Landau levels are found to emerge…
We discuss several applications and extensions of our previous operator solution of the $N$-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i -…
We study the universal long-distance behaviour of the Laughlin state for the fractional quantum Hall effect and the ground state of the Calogero-Sutherland model (one dimensional $1/r^2$ interaction model). In particular, it is shown that…
A twistor model is proposed for the free relativistic anyon. The Hamiltonian reduction of this model by the action of the spin generator leads to the minimal covariant model; whereas that by the action of spin and mass generators, to the…
Electrons in strong magnetic fields can be described by one-dimensional models in which the Coulomb potential and interactions are replaced by regularizations associated with the lowest Landau band. For a large class of models of these…
We show that a particular many-matrix model gives rise, upon hamiltonian reduction, to a multidimensional version of the Calogero-Sutherland model and its spin generalizations. Some simple solutions of these models are demonstrated by…
We study nematic liquid crystalline films within the framework of the Landau-de Gennes theory in the limit when both the thickness of the film and the nematic correlation length are vanishingly small compared to the lateral extent of the…
Explicit relation between Laughlin state of the quantum Hall effect and one-dimensional(1D) model with long-ranged interaction ($1/r^2$) is discussed. By rewriting lowest Landau level wave functions in terms of 1D representation, Laughlin…
We study the ground state of a large number N of 2D anyons in an external magnetic field. We consider a scaling limit where the statistics parameter $\alpha$ tends to zero when N tends to infinity which allows the statistics to be seen as a…
We consider the quantum mechanics of an electron trapped on an infinite band along the $x$-axis in the presence of the Morse-like perpendicular magnetic field $\vec{B}=-B_{0}e^{-\frac{2\pi}{a_{0}}x}\hat{k}$ with $B_{0}>0$ as a constant…
Conformally related metrics and Lagrangians are considered in the context of scalar-tensor gravity cosmology. After the discussion of the problem, we pose a lemma in which we show that the field equations of two conformally related…
The deviation of the energy position of a delocalized state from the center of Landau level is studied in the framework of the Chalker-Coddington model. It is demonstrated that introducing a weak Landau level mixing results in a shift of…
Magnetic reconnection occurs when two plasmas having co-planar but anti-parallel magnetic fields meet. At the contact point, the field is locally annihilated and the magnetic energy can be released into the surrounding plasma. Theory and…
The planar Landau system which describes the quantum mechanical motion of a charged particle in a plane with a uniform magnetic field perpendicular to the plane, is explored within pedagogical settings aimed at the beginning graduate level.…
We study two-particle coherent states and their dynamics in the lowest Landau level (LLL) under the influence of quadratic potentials. We focus on generalized coherent states that describe Abelian anyons in the LLL and are associated with…
A review on the Anyon model and the lowest Landau level Anyon model is presented.