5,557 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
The theory of coherent dynamic nuclear polarization in quantum dots
We consider the dynamic nuclear spin polarization (DNP) using two electrons
in a double quantum dot in presence of external magnetic field and spin-orbit
interaction, in various schemes of periodically repeated sweeps through the
S-T+ avoided crossing. By treating the problem semi-classically, we find that
generally the DNP have two distinct contributions - a geometrical polarization
and a dynamic polarization, which have different dependence on the control
parameters such as the sweep rates and waiting times in each period. Both terms
show non-trivial dependence on those control parameter. We find that even for
small spin-orbit term, the dynamical polarization dominates the DNP in presence
of a long waiting period near the S-T+ avoided crossing, of the order of the
nuclear Larmor precession periods. A detailed numerical analysis of a specific
control regime can explain the oscillations observed by Foletti et.~al.~in
arXiv:0801.3613.Comment: 22 pages, 6 figure
Composite Fermions in Modulated Structures: Transport and Surface Acoustic Waves
Motivated by a recent experiment of Willett et al. [Phys. Rev. Lett. 78, 4478
(1997)], we employ semiclassical composite-fermion theory to study the effect
of a periodic density modulation on a quantum Hall system near Landau level
filling factor nu=1/2. We show that even a weak density modulation leads to
dramatic changes in surface-acoustic-wave (SAW) propagation, and propose an
explanation for several key features of the experimental observations. We
predict that properly arranged dc transport measurements would show a structure
similar to that seen in SAW measurements.Comment: Version published in Phys. Rev. Lett. Figures changed to show SAW
velocity shift. LaTeX, 5 pages, two included postscript figure
Ground state, quasi-hole, a pair of quasihole wavefunctions and instability in bilayer quantum Hall systems
Bilayer quantum Hall system (BLQH) differ from its single layer counterparts
(SLQH) by its symmetry breaking ground state and associated neutral gapless
mode in the pseudo-spin sector. Due to the gapless mode, qualitatively good
groundstate and low energy excited state wavefunctions at any finite distance
is still unknown. We investigate this important open problem by the Composite
Boson (CB) theory developed by one of the authors to study BLQH systematically.
We derive the ground state, quasi-hole and a pair of quasihole wavefunctions
from the CB theory and its dual action. We find that the ground state
wavefunction differs from the well known wavefunction at any finite . In addition to commonly known multiplicative factors, the quasi-hole and a
pair of quasi-holes wavefunctions also contain non-trivial normalization
factors multiplying the correct ground state wavefunction. All the distance
dependencies in all the wavefunctions are encoded in the spin part of the
ground state wavefunction. The instability encoded in the spin part of the
groundstate wavefunction leads to the pseudo-spin density wave formation
proposed by one of the authors previously. Some subtleties related to the
Lowest Landau Level (LLL) projection of the wavefunctions are briefly
discussed.Comment: 9 pages, 1 figure, REVTEX, Final version to appear in Phys. Rev.
A number conserving theory for topologically protected degeneracy in one-dimensional fermions
Semiconducting nanowires in proximity to superconductors are among promising
candidates to search for Majorana fermions and topologically protected
degeneracies which may ultimately be used as building blocks for topological
quantum computers. The prediction of neutral Majorana fermions in the
proximity-induced superconducting systems ignores number-conservation and thus
leaves open the conceptual question of how a topological degeneracy that is
robust to all local perturbations arises in a number-conserving system. In this
work, we study how local attractive interactions generate a topological
ground-state near-degeneracy in a quasi one-dimensional superfluid using
bosonization of the fermions. The local attractive interactions opens a
topological quasiparticle gap in the odd channel wires (with more than one
channel) with end Majorana modes associated with a topological near-degeneracy.
We explicitly study the robustness of the topological degeneracy to local
perturbations and find that such local perturbations result in quantum phase
slips which split of the topological degeneracy by an amount that does not
decrease exponentially with the length of the wire, but still decreases rapidly
if the number of channels is large. Therefore a bulk superconductor with a
large number of channels is crucial for true topological degeneracy.Comment: 11 pages, 2 figure
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