Comment on "Statistical Mechanics of Non-Abelian Chern-Simons Particles"

The second virial coefficient for non-Abelian Chern-Simons particles is recalculated. It is shown that the result is periodic in the flux parameter just as in the Abelian theory.Comment: 3 pages, latex fil

Universality of the Wigner time delay distribution for one-dimensional random potentials

We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out on samples whose sizes are large compared to the localisation length (localised regime). The case of small samples is also discussed (ballistic regime). We provide a physical argument which explains in a quantitative way the origin of the exponential divergence of the moments. The occurence of a log-normal tail for finite size systems is analysed. Finally, we present exact results in the low energy limit which clearly show a departure from the universal behaviour.Comment: 4 pages, 3 PostScript figure

Exact Solution of the one-impurity quantum Hall problem

The problem of a non-relativistic electron in the presence of a uniform electromagnetic field and of one impurity, described by means of an Aharonov-Bohm point-like vortex, is studied. The exact solution is found and the quantum Hall's conductance turns out to be the same as in the impurity-free case. This exactly solvable model seems to give indications, concerning the possible microscopic mechanisms underlying the integer quantum Hall effect, which sensibly deviate from some proposals available in the literature.Comment: 25 pages, TeX, to appear in J. Phys.

Laughlin states on the Poincare half-plane and its quantum group symmetry

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 calculate the corresponding filling factor by using the plasma analogy of the FQHE.Comment: 9 pages,Late

Finite-size anyons and perturbation theory

We address the problem of finite-size anyons, i.e., composites of charges and finite radius magnetic flux tubes. Making perturbative calculations in this problem meets certain difficulties reminiscent of those in the problem of pointlike anyons. We show how to circumvent these difficulties for anyons of arbitrary spin. The case of spin 1/2 is special because it allows for a direct application of perturbation theory, while for any other spin, a redefinition of the wave function is necessary. We apply the perturbative algorithm to the N-body problem, derive the first-order equation of state and discuss some examples.Comment: 18 pages (RevTex) + 4 PS figures (all included); a new section on equation of state adde

Numerical studies of planar closed random walks

Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension $d_H=4/3$. However, when properly defined by taking into account the inner 0-winding sectors, the frontiers of the random walks have a Hausdorff dimension $d_H\approx 1.77$.Comment: 15 pages, 15 figure

Elasticity model of a supercoiled DNA molecule

Within a simple elastic theory, we study the elongation versus force characteristics of a supercoiled DNA molecule at thermal equilibrium in the regime of small supercoiling. The partition function is mapped to the path integral representation for a quantum charged particle in the field of a magnetic monopole with unquantized charge. We show that the theory is singular in the continuum limit and must be regularised at an intermediate length scale. We find good agreement with existing experimental data, and point out how to measure the twist rigidity accurately.Comment: Latex, 4 pages. The figure contains new experimental data, giving a new determination of the twist rigidit

Relativistic center-vortex dynamics of a confining area law

We offer a physicists' proof that center-vortex theory requires the area in the Wilson-loop area law to involve an extremal area. Area-law dynamics is determined by integrating over Wilson loops only, not over surface fluctuations for a fixed loop. Fluctuations leading to to perimeter-law corrections come from loop fluctuations as well as integration over finite -thickness center-vortex collective coordinates. In d=3 (or d=2+1) we exploit a contour form of the extremal area in isothermal which is similar to d=2 (or d=1+1) QCD in many respects, except that there are both quartic and quadratic terms in the action. One major result is that at large angular momentum \ell in d=3+1 the center-vortex extremal-area picture yields a linear Regge trajectory with Regge slope--string tension product \alpha'(0)K_F of 1/(2\pi), which is the canonical Veneziano/string value. In a curious effect traceable to retardation, the quark kinetic terms in the action vanish relative to area-law terms in the large-\ell limit, in which light-quark masses \sim K_F^{1/2} are negligible. This corresponds to string-theoretic expectations, even though we emphasize that the extremal-area law is not a string theory quantum-mechanically. We show how some quantum trajectory fluctuations as well as non-leading classical terms for finite mass yield corrections scaling with \ell^{-1/2}. We compare to old semiclassical calculations of relativistic q\bar{q} bound states at large \ell, which also yield asymptotically-linear Regge trajectories, finding agreement with a naive string picture (classically, not quantum-mechanically) and disagreement with an effective-propagator model. We show that contour forms of the area law can be expressed in terms of Abelian gauge potentials, and relate this to old work of Comtet.Comment: 20 pages RevTeX4 with 3 .eps figure

Quantum group symmetry of the Quantum Hall effect on the non-flat surfaces

After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a first example we show that the $su(2)$ symmetry of the QHE on sphere leads to $su_q(2)$ algebra in the equator . We explain this result by a contraction of $su(2)$ . Secondly , with the help of the symmetry operators of QHE on the Pioncare upper half plane , we will show that the ground state wave functions form a representation of the $su_q(2)$ algebra .Comment: 8 pages,latex,no figur

Coulomb gas representation of quantum Hall effect on Riemann surfaces

Using the correlation function of chiral vertex operators of the Coulomb gas model, we find the Laughlin wavefunctions of quantum Hall effect, with filling factor $\nu =1/m$, on Riemann sufaces with Poincare metric. The same is done for quasihole wavefunctions. We also discuss their plasma analogy.Comment: 10 pages, LaTex, the paper is completely rewritten, It will be appeared in : Jour. Phys. A 32 (1999