Fractional statistic

We improve Haldane's formula which gives the number of configurations for $N$ particles on $d$ states in a fractional statistic defined by the coupling $g=l/m$. Although nothing is changed in the thermodynamic limit, the new formula makes sense for finite $N=pm+r$ with $p$ integer and $0<r\leq m.$ A geometrical interpretation of fractional statistic is given in terms of ''composite particles''.Comment: flatex hald.tex, 3 files Submitted to: Phys. Rev.

Incidence of the boundary shape in the effective theory of fractional quantum Hall edges

Starting from a microscopic description of a system of strongly interacting electrons in a strong magnetic field in a finite geometry, we construct the boundary low energy effective theory for a fractional quantum Hall droplet taking into account the effects of a smooth edge. The effective theory obtained is the standard chiral boson theory (chiral Luttinger theory) with an additional self-interacting term which is induced by the boundary. As an example of the consequences of this model, we show that such modification leads to a non-universal reduction in the tunnelling exponent which is independent of the filling fraction. This is in qualitative agreement with experiments, that systematically found exponents smaller than those predicted by the ordinary chiral Luttinger liquid theory.Comment: 12 pages, minor changes, replaced by published versio

Spin-Charge Separation at Finite Temperature in the Supersymmetric t-J Model with Long-Range Interactions

Thermodynamics is derived rigorously for the 1D supersymmetric {\it t-J} model and its SU($K,1$) generalization with inverse-square exchange. The system at low temperature is described in terms of spinons, antispinons, holons and antiholons obeying fractional statistics. They are all free and make the spin susceptibility independent of electron density, and the charge susceptibility independent of magnetization. Thermal spin excitations responsible for the entropy of the SU($K,1$) model are ascribed to free para-fermions of order $K-1$.Comment: 10 pages, REVTE

Non-Commutative Corrections to the MIC-Kepler Hamiltonian

Non-commutative corrections to the MIC-Kepler System (i.e. hydrogen atom in the presence of a magnetic monopole) are computed in Cartesian and parabolic coordinates. Despite the fact that there is no simple analytic expression for non-commutative perturbative corrections to the MIC-Kepler spectrum, there is a term that gives rise to the linear Stark effect which didn't exist in the standard hydrogen model.Comment: 5 page

Exchange Operator Formalism for Integrable Systems of Particles

We formulate one dimensional many-body integrable systems in terms of a new set of phase space variables involving exchange operators. The hamiltonian in these variables assumes a decoupled form. This greatly simplifies the derivation of the conserved charges and the proof of their commutativity at the quantum level.Comment: 8 page

Inhomogeneous Condensates in Planar QED

We study the formation of vacuum condensates in $2+1$ dimensional QED in the presence of inhomogeneous background magnetic fields. For a large class of magnetic fields, the condensate is shown to be proportional to the inhomogeneous magnetic field, in the large flux limit. This may be viewed as a {\it local} form of the {\it integrated} degeneracy-flux relation of Aharonov and Casher.Comment: 13 pp, LaTeX, no figures; to appear in Phys. Rev.

Composite fermion wave functions as conformal field theory correlators

It is known that a subset of fractional quantum Hall wave functions has been expressed as conformal field theory (CFT) correlators, notably the Laughlin wave function at filling factor $\nu=1/m$ ($m$ odd) and its quasiholes, and the Pfaffian wave function at $\nu=1/2$ and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at $\nu=1/m$ are created by inserting anyonic vertex operators, $P_{\frac{1}{m}}(z)$, that replace a subset of the electron operators in the correlator. The one-quasiparticle wave function is identical to the corresponding CF wave function, and the two-quasiparticle wave function has correct fractional charge and statistics and is numerically almost identical to the corresponding CF wave function. We further show how to exactly represent the CF wavefunctions in the Jain series $\nu = s/(2sp+1)$ as the CFT correlators of a new type of fermionic vertex operators, $V_{p,n}(z)$, constructed from $n$ free compactified bosons; these operators provide the CFT representation of composite fermions carrying $2p$ flux quanta in the $n^{\rm th}$ CF Landau level. We also construct the corresponding quasiparticle- and quasihole operators and argue that they have the expected fractional charge and statistics. For filling fractions 2/5 and 3/7 we show that the chiral CFTs that describe the bulk wave functions are identical to those given by Wen's general classification of quantum Hall states in terms of $K$-matrices and $l$- and $t$-vectors, and we propose that to be generally true. Our results suggest a general procedure for constructing quasiparticle wave functions for other fractional Hall states, as well as for constructing ground states at filling fractions not contained in the principal Jain series.Comment: 26 pages, 3 figure

On Some One-Parameter Families of Three-Body Problems in One Dimension: Exchange Operator Formalism in Polar Coordinates and Scattering Properties

We apply the exchange operator formalism in polar coordinates to a one-parameter family of three-body problems in one dimension and prove the integrability of the model both with and without the oscillator potential. We also present exact scattering solution of a new family of three-body problems in one dimension.Comment: 10 pages, LaTeX, no figur

Supertraces on the algebra of observables of the rational Calogero model based on the classical root system

A complete set of supertraces on the algebras of observables of the rational Calogero models with harmonic interaction based on the classical root systems of B_N, C_N and D_N types is found. These results extend the results known for the case A_N. It is shown that there exist Q independent supertraces where Q(B_N)=Q(C_N) is a number of partitions of N into a sum of positive integers and Q(D_N) is a number of partitions of N into a sum of positive integers with even number of even integers.Comment: 10 pages, LATE

Noncommutative effective theory of vortices in a complex scalar field

We derive a noncommutative theory description for vortex configurations in a complex field in 2+1 dimensions. We interpret the Magnus force in terms of the noncommutativity, and obtain some results for the quantum dynamics of the system of vortices in that context