4,789 research outputs found
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 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, , some
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
Spontaneous Currents in Spinless Fermion Lattice Models at the Strong-Coupling Limit
What kind of lattice Hamiltonian manifestly has an ordered state with
spontaneous orbital currents? We consider interacting spinless fermions on an
array of square plaquettes, connected by weak hopping; the array geometry may
be a 2 x 2L ladder, a 2 x 2 x 2L "tube", or a 2L x 2L square grid. At half
filling, we derive an effective Hamiltonian in terms of pseudospins, of which
one component represents orbital currents, and find the conditions sufficient
for orbital current long-range order. We consider spinfull variants of the
aforesaid spinless models and make contact with other spinfull models in the
literature purported to possess spontaneous currents.Comment: added two new references following recent communicatio
Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
We report the observation of a new series of Abelian and non-Abelian
topological states in fractional Chern insulators (FCI). The states appear at
bosonic filling nu= k/(C+1) (k, C integers) in several lattice models, in
fractionally filled bands of Chern numbers C>=1 subject to on-site Hubbard
interactions. We show strong evidence that the k=1 series is Abelian while the
k>1 series is non-Abelian. The energy spectrum at both groundstate filling and
upon the addition of quasiholes shows a low-lying manifold of states whose
total degeneracy and counting matches, at the appropriate size, that of the
Fractional Quantum Hall (FQH) SU(C) (color) singlet k-clustered states
(including Halperin, non-Abelian spin singlet states and their
generalizations). The groundstate momenta are correctly predicted by the FQH to
FCI lattice folding. However, the counting of FCI states also matches that of a
spinless FQH series, preventing a clear identification just from the energy
spectrum. The entanglement spectrum lends support to the identification of our
states as SU(C) color-singlets but offers new anomalies in the counting for
C>1, possibly related to dislocations that call for the development of new
counting rules of these topological states.Comment: 12 pages with supplemental material, 20 figures, published versio
Abelian and non-abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect
We study the quantum anomalous Hall effect described by a class of
two-component Haldane models on square lattices. We show that the latter can be
transformed into a pseudospin triplet p+ip-wave paired superfluid. In the long
wave length limit, the ground state wave function is described by Halperin's
(1,1,-1) state of neutral fermions analogous to the double layer quantum Hall
effect. The vortex excitations are charge e/2 abelian anyons which carry a
neutral Dirac fermion zero mode. The superconducting proximity effect induces
`tunneling' between `layers' which leads to topological phase transitions
whereby the Dirac fermion zero mode fractionalizes and Majorana fermions emerge
in the edge states. The charge e/2 vortex excitation carrying a Majorana zero
mode is a non-abelian anyon. The proximity effect can also drive a conventional
insulator into a quantum anomalous Hall effect state with a Majorana edge mode
and the non-abelian vortex excitations.Comment: 6 pages, 4 figures, accepted by Phys. Rev.
Fractional Chern Insulators beyond Laughlin states
We report the first numerical observation of composite fermion (CF) states in
fractional Chern insulators (FCI) using exact diagonalization. The ruby lattice
Chern insulator model for both fermions and bosons exhibits a clear signature
of CF states at filling factors 2/5 and 3/7 (2/3 and 3/4 for bosons). The
topological properties of these states are studied through several approaches.
Quasihole and quasielectron excitations in FCI display similar features as
their fractional quantum hall (FQH) counterparts. The entanglement spectrum of
FCI groundstates shows an identical fingerprint to its FQH partner. We show
that the correspondence between FCI and FQH obeys the emergent symmetry already
established, proving the validity of this approach beyond the clustered states.
We investigate other Chern insulator models and find similar signatures of CF
states. However, some of these systems exhibit strong finite size effects.Comment: 9 pages with supplementary material, 13 figures, published versio
Nonlinear field-dependence and f-wave interactions in superfluid 3He
We present results of transverse acoustics studies in superfluid ^{3}He-B at
fields up to 0.11 T. Using acoustic cavity interferometry, we observe the
Acoustic Faraday Effect for a transverse sound wave propagating along the
magnetic field, and we measure Faraday rotations of the polarization as large
as 1710^{\circ}. We use these results to determine the Zeeman splitting of the
Imaginary Squashing mode, an order parameter collective mode with total angular
momentum J=2. We show that the pairing interaction in the f-wave channel is
attractive at a pressure of P=6 bar. We also report nonlinear field dependence
of the Faraday rotation at frequencies substantially above the mode frequency
not accounted for in the theory of the transverse acoustic dispersion relation
formulated for frequencies near the mode. Consequently, we have identified the
region of validity of the theory allowing us to make corrections to the
analysis of Faraday rotation experiments performed in earlier work.Comment: 7 pages, 5 figure
Parity Effect in a Small Superconducting Particle
Matveev and Larkin calculated the parity effect on the ground state energy of
a small superconducting particle in the regimes where the mean level spacing is
either large or small compared to the bulk gap. We perform a numerical
calculation which extends their results into the intermediate regime, where the
level spacing is of the same order as the bulk gap.Comment: 6 LaTeX pages, including 2 EPS figures; corrected reference and
spellin
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