相关论文: Laughlin states on the sphere as representations o…
We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We…
The quantum mechanics of a system of charged particles interacting with a magnetic field on Riemann surfaces is studied. We explicitly construct the wave functions of ground states in the case of a metric proportional to the Chern form of…
In two space dimensions the possibilities of fractional spin as well as fractional statistics exist. I examine the relation between fractional spin and statistics for Laughlin quasi-particles in a two-dimensional electron system with…
An algebraic formalism for description of quantum states of charged particle with spin moving in two-dimensional space under influence of singular magnetic field is developed in terms of graded algebras. The fundamental assumption is that…
When the parameter of deformation q is a m-th root of unity, the centre of U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new generators, which are basically the m-th powers of all the Cartan generators of U_q(sl(N)).…
We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system.…
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…
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 demonstrate that the two-dimensonal electron system in a strong perpendicular magnetic field has stable states which break rotational but not translational symmetry. The Laughlin fluid becomes unstable to these states in quantum wells…
The Laughlin state is an ansatz for the ground state of a system of 2D quantum particles submitted to a strong magnetic field and strong interactions. The two effects conspire to generate strong and very specific correlations between the…
An analytical solution of the quantum problem of an electron on a spherical segment with angular confinement potential of the form of rectangular impenetrable walls is presented. It is shown that the problem is reduced to finding solution…
It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive…
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.
The second-quantized form of the Laughlin states for the fractional quantum Hall effect is discussed by decomposing the Laughlin wavefunctions into the $N$-particle Slater basis. A general formula is given for the expansion coefficients in…
Quantum groups at roots of unity have the property that their centre is enlarged. Polynomial equations relate the standard deformed Casimir operators and the new central elements. These relations are important from a physical point of view…
Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until…
We present a thorough analysis of the electron density distribution (shape) of two electrons, confined in the three-dimensional harmonic oscillator potential, as a function of the perpendicular magnetic field.Explicit algebraic expressions…
We define a two-parameter deformation of the quasi-shuffle by means of the formal group law associated with the exponential generating function of the homogeneous Eulerian polynomials, and construct bases of $QSym$ and $\WQSym$ whose…
A $q$-deformed free spinning relativistic particle is discussed in the framework of the Lagrangian formalism. Three equivalent Lagrangians are obtained for this system which are endowed with $q$-deformed local (super)gauge symmetries and…
We study quantum deformed $gl(n)$ and $igl(n)$ algebras on a quantum space discussing multi-parametric extension. We realize elements of deformed $gl(n)$ and $igl(n)$ algebras by a quantum fermionic space. We investigate a map between…