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 $k(r)$

Proposed experiments to probe the non-abelian \nu=5/2 quantum Hall state

We propose several experiments to test the non-abelian nature of quasi-particles in the fractional quantum Hall state of \nu=5/2. One set of experiments studies interference contribution to back-scattering of current, and is a simplified version of an experiment suggested recently. Another set looks at thermodynamic properties of a closed system. Both experiments are only weakly sensitive to disorder-induced distribution of localized quasi-particles.Comment: Additional references and an improved figure, 5 page

Fractional quantum Hall effect at ν=5/2\nu = 5/2: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model

We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction $\nu = 5/2$, based on the disc geometry. Our model includes Coulomb interaction and a semi-realistic confining potential. We also mix in some three-body interaction in some cases to help elucidate the physics. We obtain a phase diagram, discuss the conditions under which the ground state can be described by the Moore-Read state, and study its competition with neighboring stripe phases. We also study quasihole excitations and edge excitations in the Moore-Read--like state. From the evolution of edge spectrum, we obtain the velocities of the charge and neutral edge modes, which turn out to be very different. This separation of velocities is a source of decoherence for a non-Abelian quasihole/quasiparticle (with charge $\pm e/4$) when propagating at the edge; using numbers obtained from a specific set of parameters we estimate the decoherence length to be around four microns. This sets an upper bound for the separation of the two point contacts in a double point contact interferometer, designed to detect the non-Abelian nature of such quasiparticles. We also find a state that is a potential candidate for the recently proposed anti-Pfaffian state. We find the speculated anti-Pfaffian state is favored in weak confinement (smooth edge) while the Moore-Read Pfaffian state is favored in strong confinement (sharp edge).Comment: 15 pages, 9 figures; Estimate of e/4 quasiparticle/hole coherence length when propagating along the edge modified in response to a recent revision of Ref. 25, and minor changes elsewher

Composite Fermions with Orbital Magnetization

For quantum Hall systems, in the limit of large magnetic field (or equivalently small electron band mass $m_b$), the static response of electrons to a spatially varying magnetic field is largely determined by kinetic energy considerations. This response is not correctly given in existing approximations based on the Fermion Chern-Simons theory of the partially filled Landau level. We remedy this problem by attaching an orbital magnetization to each fermion to separate the current into magnetization and transport contributions, associated with the cyclotron and guiding center motions respectively. This leads to a Chern-Simons Fermi liquid description of the $\nu=\frac{1}{2m}$ state which correctly predicts the $m_b$ dependence of the static and dynamic response in the limit $m_b \rightarrow 0$.Comment: 4 pages, RevTeX, no figure

Theory of the Three Dimensional Quantum Hall Effect in Graphite

We predict the existence of a three dimensional quantum Hall effect plateau in a graphite crystal subject to a magnetic field. The plateau has a Hall conductivity quantized at $\frac{4e^2}{\hbar} \frac{1}{c_0}$ with $c_0$ the c-axis lattice constant. We analyze the three-dimensional Hofstadter problem of a realistic tight-binding Hamiltonian for graphite, find the gaps in the spectrum, and estimate the critical value of the magnetic field above which the Hall plateau appears. When the Fermi level is in the bulk Landau gap, Hall transport occurs through the appearance of chiral surface states. We estimate the magnetic field necessary for the appearance of the three dimensional quantum Hall Effect to be $15.4$T for electron carriers and $7.0$T for hole carriers.Comment: Several new references adde

Effect of n+-GaAs thickness and doping density on spin injection of GaMnAs/n+-GaAs Esaki tunnel junction

We investigated the influence of n+-GaAs thickness and doping density of GaMnAs/n+-GaAs Esaki tunnel junction on the efficiency of the electrical electron spin injection. We prepared seven samples of GaMnAs/n+-GaAs tunnel junctions with different n+-GaAs thickness and doping density grown on identical p-AlGaAs/p-GaAs/n-AlGaAs light emitting diode (LED) structures. Electroluminescence (EL) polarization of the surface emission was measured under the Faraday configuration with external magnetic field. All samples have the bias dependence of the EL polarization, and higher EL polarization is obtained in samples in which n+-GaAs is completely depleted at zero bias. The EL polarization is found to be sensitive to the bias condition for both the (Ga,Mn)As/n+-GaAs tunnel junction and the LED structure.Comment: 4pages, 4figures, 1table, To appear in Physica

Superconductivity and Abelian Chiral Anomalies

Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate condensate bands for unitary order, which are realizations of Abelian chiral anomalies for non-Abelian connections. The three types of Chern numbers for the $x,y$ and $z$-directions are given by covering degrees of some doubled surfaces around the Dirac monopoles. For nonunitary states, several topological invariants are defined by analyzing the so-called $q$-helicity. Topological origins of the nodal structures of superconducting gaps are also discussed.Comment: An example with a figure and discussions are supplemente

Magneto-acoustic rotation of transverse waves in 3He-B

In superfluid 3He-B the off-resonant coupling of the J=2-, M=+/- 1 order parameter collective modes to transverse current excitations stabilizes propagating transverse waves with low damping for frequencies above that of the J=2- modes. Right- (RCP) and left circularly polarized (LCP) transverse modes are degenerate in zero field; however, a magnetic field with H || q lifts this degeneracy giving rise to the acoustic analog of circular birefringence and an acoustic Faraday effect for linearly polarized transverse sound waves. We present theoretical results for the temperature, pressure and field dependence of the Faraday rotation angle, and compare the theory with recent measurements. The analysis provides a direct measurement of the Lande' g-factor for the J=2- modes, and new information on the magnitude of f-wave pairing correlations in 3He-B.Comment: Submitted to Physica B (Proc. LT22), 2 pages with 1 figur

Anti-Fall: A Non-intrusive and Real-time Fall Detector Leveraging CSI from Commodity WiFi Devices

Fall is one of the major health threats and obstacles to independent living for elders, timely and reliable fall detection is crucial for mitigating the effects of falls. In this paper, leveraging the fine-grained Channel State Information (CSI) and multi-antenna setting in commodity WiFi devices, we design and implement a real-time, non-intrusive, and low-cost indoor fall detector, called Anti-Fall. For the first time, the CSI phase difference over two antennas is identified as the salient feature to reliably segment the fall and fall-like activities, both phase and amplitude information of CSI is then exploited to accurately separate the fall from other fall-like activities. Experimental results in two indoor scenarios demonstrate that Anti-Fall consistently outperforms the state-of-the-art approach WiFall, with 10% higher detection rate and 10% less false alarm rate on average.Comment: 13 pages,8 figures,corrected version, ICOST conferenc

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