Related papers: A Mean Field Theory for the Quantum Hall Liquid. I…
An effective Chern-Simons theory for the quantum Hall states with edges is studied by treating the edge and bulk properties in a unified fashion. An exact steady-state solution is obtained for a half-plane geometry using the Wiener-Hopf…
I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields…
We consider Mckean-Vlasov type stochastic differential equations with multiplicative noise arising from the random vortex method. Such an equation can be viewed as the mean-field limit of interacting particle systems with singular…
Collective modes of exotic quantum fluids reveal underlying physical mechanisms responsible for emergent complex quantum ground states. We observe unexpected new collective modes in the fractional quantum Hall (FQH) regime:…
Reports of weak local minima in the magnetoresistance at $\nu=2+3/5$, $2+3/7$, $2+4/9$, $2+5/9$, $2+5/7$, and $2+5/8$ in the second Landau level of the electron gas in GaAs/AlGaAs left open the possibility of fractional quantum Hall states…
We present the solution to London's equations for the magnetic fields of a vortex oriented parallel to the plane, and normal to a crystal face, of a layered superconductor. These expressions account for flux spreading at the superconducting…
We use the voltage biased tip of a scanning force microscope at a temperature of 35\,mK to locally induce the fractional quantum Hall state of $\nu=1/3$ in a split-gate defined constriction. Different tip positions allow us to vary the…
Nearly parallel vortex filaments are a generalization of point vortices and describe many phenomena under conservation of angular momentum including vortices forming in deep ocean convection, magnetically confined plasmas, and the solar…
The set of the nonlinear Ginzburg-Landau equations is solved for an Al mesoscopic superconducting triangle of finite thickness. We calculate the distributions of the superconducting phase in the triangle and of the magnetic field in and…
Inspired by recent experiments by Geim et al. we discuss the classical theory of the Hall effect of a 2 dimensional electron gas in an inhomogeneous magnetic field. The field modulation is in the form of flux tubes created by a…
A variational $\nu=2/3$ state, which unifies the sharp edge picture of MacDonald with the soft edge picture of Chang and of Beenakker is presented and studied in detail. Using an exact relation between correlation functions of this state…
As a model for the transitions between plateaus in the fractional Quantum Hall effect we study the critical behavior of non-interacting charged particles in a static random magnetic field with finite mean value. We argue that this model…
Alternative forms of the solutions to the quantum field equations and their implications for physical theory are considered. Incorporation of these alternative solution forms, herein deemed "supplemental solutions", into the development of…
In superconductors with three or more components, time-reversal symmetry may be broken when the inter-component couplings are repulsive, leading to a superconducting state with two-fold degeneracy. When prepared carefully there is a stable…
We have investigated the fractional quantum Hall states for the Dirac electrons in a graphene layer in different Landau levels. The relativistic nature of the energy dispersion relation of the electrons in the graphene significantly…
At high temperatures the A_0 component of the Yang--Mills field plays the role of the Higgs field, and the 1-loop potential V(A_0) plays the role of the Higgs potential. We find a new stable vortex solution of the Abrikosov-Nielsen-Olesen…
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.
We write a Ginzburg-Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2+1 dimensions. Using the method of Lund we derive a collective coordinate action for vortex defects in the order…
We study conformal field theories describing two massless one-dimensional fields interacting at a single spatial point. The interactions we include are periodic functions of the bosonized fields separately plus a ``magnetic'' interaction…
We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional…