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The composite-fermion approach as formulated in Fermion Chern-Simons theory has been very successful in describing the physics of the lowest Landau level near Landau level filling factor v=1/2. Recent work has emphasized the fact that the true low energy quasiparticles at this filling factor are electrically neutral and carry an, electric dipole moment. In a previous work, we discussed at length two formulations in terms of dipolar quasiparticles. Here we briefly, review one approach—termed electron-centered quasiparticles—and show how it can be extended from v=1/2 to nearby filling factors v where the low-energy quasiparticles carry both an electric dipole moment and an overall charge e*=(2v-1)e. [ABSTRACT FROM AUTHOR]

The winding of a single polymer in thermal equilibrium around a repulsive cylindrical obstacle is perhaps the simplest example of statistical mechanics in a multiply connected geometry. As shown by S.F. Edwards, this problem is closely related to the quantum mechanics of a charged particle interacting with a Aharonov-Bohm flux. In another development, Pollock and Ceperley have shown that boson world lines in 2+1 dimensions with periodic boundary conditions, regarded as ring polymers on a torus, have a mean square winding number given by =2nsħ2/mkBT, where m is the boson mass and ns is the superfluid number density. Here, we review the mapping of the statistical mechanics of polymers with constraints onto quantum mechanics, and show that there is an interesting generalization of the Pollock-Ceperley result to directed polymer melts interacting with a repulsive rod of radius a. When translated into boson language, the mean square winding number around the rod for a system of size R perpendicular to the rod reads $$\left\langle {W^2 } \right\rangle = \frac{{n_s \hbar ^2 }}{{2\pi mk_B T}}\ln (R/a)$$ . This result is directly applicable to vortices in Type II superconductors in the presence of columnar defects. An external current passing through the rod couples directly to the winding number in this case. [ABSTRACT FROM AUTHOR]