Graded Lie algebras with finite polydepth

If A is a graded connected algebra then we define a new invariant, polydepth A, which is finite if $Ext_A^*(M,A) \neq 0$ for some A-module M of at most polynomial growth. Theorem 1: If f : X \to Y is a continuous map of finite category, and if the orbits of H_*(\Omega Y) acting in the homology of the homotopy fibre grow at most polynomially, then H_*(\Omega Y) has finite polydepth. Theorem 2: If L is a graded Lie algebra and polydepth UL is finite then either L is solvable and UL grows at most polynomially or else for some integer d and all r, $\sum_{i=k+1}^{k+d} {dim} L_i \geq k^r$, $k\geq$ some $k(r)$

Quasihole condensates in quantum Hall liquids

We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states, and to several classes of non-Abelian hierarchical states. Most previously proposed spin-polarized quantum Hall wave functions appear as special cases. In this paper we explain the physical motivations for the approach, and exemplify it by explicitly constructing the level-two quasihole condensate state at filling fraction 2/3, and the two level-three states at 5/13 and 5/7 which are built from combinations of quasielectron and quasihole condensates.Comment: 16 page

Quantum Hall Phase Diagram of Second Landau-level Half-filled Bilayers: Abelian versus Non-Abelian States

The quantum Hall phase diagram of the half-filled bilayer system in the second Landau level is studied as a function of tunneling and layer separation using exact diagonalization. We make the striking prediction that bilayer structures would manifest two distinct branches of incompressible fractional quantum Hall effect (FQHE) corresponding to the Abelian 331 state (at moderate to low tunneling and large layer separation) and the non-Abelian Pfaffian state (at large tunneling and small layer separation). The observation of these two FQHE branches and the quantum phase transition between them will be compelling evidence supporting the existence of the non-Abelian Pfaffian state in the second Landau level.Comment: 4 pages, 3 figure

Imaginary Squashing Mode Spectroscopy of Helium Three B

We have made precision measurements of the frequency of a collective mode of the superfluid 3He-B order parameter, the J=2- imaginary squashing mode. Measurements were performed at multiple pressures using interference of transverse sound in an acoustic cavity. Transverse waves propagate in the vicinity of this order parameter mode owing to off-resonant coupling. At the crossing of the sound mode and the order parameter mode, the sound wave is strongly attenuated. We use both velocity and attenuation measurements to determine precise values of the mode frequency with a resolution between 0.1% and 0.25%.Comment: 6 pages, 4 figures, submitted to proceedings of Quantum Fluids and Solids (QFS) Conference 2006; revised 9/26/0

Modification of electronic surface states by graphene islands on Cu(111)

We present a study of graphene/substrate interactions on UHV-grown graphene islands with minimal surface contamination using \emph{in situ} low-temperature scanning tunneling microscopy (STM). We compare the physical and electronic structure of the sample surface with atomic spatial resolution on graphene islands versus regions of bare Cu(111) substrate. We find that the Rydberg-like series of image potential states is shifted toward lower energy over the graphene islands relative to Cu(111), indicating a decrease in the local work function, and the resonances have a much smaller linewidth, indicating reduced coupling to the bulk. In addition, we show the dispersion of the occupied Cu(111) Shockley surface state is influenced by the graphene layer, and both the band edge and effective mass are shifted relative to bare Cu(111).Comment: 12 pages, 3 figure

The Geography of Non-formal Manifolds

We show that there exist non-formal compact oriented manifolds of dimension $n$ and with first Betti number $b_1=b\geq 0$ if and only if $n\geq 3$ and $b\geq 2$, or $n\geq (7-2b)$ and $0\leq b\leq 2$. Moreover, we present explicit examples for each one of these cases.Comment: 8 pages, one reference update

The randomly driven Ising ferromagnet, Part II: One and two dimensions

We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. In Part I, we introduced a general formalism for describing such systems and presented the mean field theory. In this article we derive results for the one dimensional case, which can be only partially solved. Monte Carlo simulations performed on a square lattice indicate that the main features of the mean field theory survive the presence of strong fluctuations.Comment: 10 pages in REVTeX/LaTeX format, 17 eps/ps figures. Submitted to Journal of Physics

Fractional quantum Hall effects in bilayers in the presence of inter-layer tunneling and charge imbalance

Two-component fractional quantum Hall systems are providing a major motivation for a large section of the physics community. Here we study two-component fractional quantum Hall systems in the spin-polarized half-filled lowest Landau level (filling factor 1/2) and second Landau level (filling factor 5/2) with exact diagonalization utilizing both the spherical and torus geometries. The two distinct two-component systems we consider are the true bilayer and effective bilayers (wide-quantum-well). In each model (bilayer and wide-quantum-well) we completely take into account inter-layer tunneling and charge imbalancing terms. We find that in the half-filled lowest Landau level, the FQHE is described by the two-component Abelian Halperin 331 state which is remarkably robust to charge imbalancing. In the half-filled second Landau, we find that the FQHE is likely described by the non-Abelian Moore-Read Pfaffian state which is also quite robust to charge imbalancing. Furthermore, we suggest the possibility of experimentally tuning from an Abelian to non-Abelian FQHE state in the second Landau level, and comment on recent experimental studies of FQHE in wide quantum well structures.Comment: 25 pages, 27 figure

The half-filled Landau level - composite fermions and dipoles

The composite-fermion approach as formulated in the fermion Chern-Simons theory has been very successful in describing the physics of the lowest Landau level near Landau level filling factor 1/2. Recent work has emphasized the fact that the true quasiparticles at these filling factors 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 1/2 to nearby filling factors where the quasiparticles carry both an electric dipole moment and an overall charge.Comment: 10 pages, minor improvements of notation and referencin