414 research outputs found
Topological pressure of simultaneous level sets
Multifractal analysis studies level sets of asymptotically defined quantities
in a topological dynamical system. We consider the topological pressure
function on such level sets, relating it both to the pressure on the entire
phase space and to a conditional variational principle. We use this to recover
information on the topological entropy and Hausdorff dimension of the level
sets.
Our approach is thermodynamic in nature, requiring only existence and
uniqueness of equilibrium states for a dense subspace of potential functions.
Using an idea of Hofbauer, we obtain results for all continuous potentials by
approximating them with functions from this subspace.
This technique allows us to extend a number of previous multifractal results
from the case to the case. We consider ergodic ratios
where the function need not be uniformly positive,
which lets us study dimension spectra for non-uniformly expanding maps. Our
results also cover coarse spectra and level sets corresponding to more general
limiting behaviour.Comment: 32 pages, minor changes based on referee's comment
Ordering of magnetic impurities and tunable electronic properties of topological insulators
We study collective behavior of magnetic adatoms randomly distributed on the
surface of a topological insulator. As a consequence of the spin-momentum
locking on the surface, the RKKY-type interactions of two adatom spins depend
on the direction of the vector connecting them, thus interactions of an
ensemble of adatoms are frustrated. We show that at low temperatures the
frustrated RKKY interactions give rise to two phases: an ordered ferromagnetic
phase with spins pointing perpendicular to the surface, and a disordered
spin-glass-like phase. The two phases are separated by a quantum phase
transition driven by the magnetic exchange anisotropy. Ferromagnetic ordering
occurs via a finite-temperature phase transition. The ordered phase breaks
time-reversal symmetry spontaneously, driving the surface states into a gapped
state, which exhibits an anomalous quantum Hall effect and provides a
realization of the parity anomaly. We find that the magnetic ordering is
suppressed by potential scattering. Our work indicates that controlled
deposition of magnetic impurities provides a way to modify the electronic
properties of topological insulators.Comment: 4+ pages, 2 figure
Exponential speed of mixing for skew-products with singularities
Let be the
endomorphism given by where is a positive real number. We prove that is
topologically mixing and if then is mixing with respect to Lebesgue
measure. Furthermore we prove that the speed of mixing is exponential.Comment: 23 pages, 3 figure
The Lyapunov spectrum is not always concave
We characterize one-dimensional compact repellers having nonconcave Lyapunov
spectra. For linear maps with two branches we give an explicit condition that
characterizes non-concave Lyapunov spectra
Developmental Role and Regulation of cortex, a Meiosis-Specific Anaphase-Promoting Complex/Cyclosome Activator
During oogenesis in metazoans, the meiotic divisions must be coordinated with development of the oocyte to ensure successful fertilization and subsequent embryogenesis. The ways in which the mitotic machinery is specialized for meiosis are not fully understood. cortex, which encodes a putative female meiosis-specific anaphase-promoting complex/cyclosome (APC/C) activator, is required for proper meiosis in Drosophila. We demonstrate that CORT physically associates with core subunits of the APC/C in ovaries. APC/CCORT targets Cyclin A for degradation prior to the metaphase I arrest, while Cyclins B and B3 are not targeted until after egg activation. We investigate the regulation of CORT and find that CORT protein is specifically expressed during the meiotic divisions in the oocyte. Polyadenylation of cort mRNA is correlated with appearance of CORT protein at oocyte maturation, while deadenylation of cort mRNA occurs in the early embryo. CORT protein is targeted for degradation by the APC/C following egg activation, and this degradation is dependent on an intact D-box in the C terminus of CORT. Our studies reveal the mechanism for developmental regulation of an APC/C activator and suggest it is one strategy for control of the female meiotic cell cycle in a multicellular organism
Thermodynamic formalism for contracting Lorenz flows
We study the expansion properties of the contracting Lorenz flow introduced
by Rovella via thermodynamic formalism. Specifically, we prove the existence of
an equilibrium state for the natural potential for the contracting Lorenz flow and for in an interval
containing . We also analyse the Lyapunov spectrum of the flow in terms
of the pressure
Quantum Charge Fluctuations in a Superconducting Grain
We consider charge quantization in a small superconducting grain that is
contacted by a normal-metal electrode and is controlled by a capacitively
coupled gate. At zero temperature and zero conductance between the grain
and the electrode, the charge as a function of the gate voltage
changes in steps. The step height is if , where and
are, respectively, the superconducting gap and the charging energy of the
grain. Quantum charge fluctuations at finite conductance remove the
discontinuity in the dependence of on and lead to a finite step width
. The resulting shape of the Coulomb blockade staircase is
of a novel type. The grain charge is a continuous function of while the
differential capacitance, , has discontinuities at certain values of
the gate voltage. We determine analytically the shape of the Coulomb blockade
staircase also at non-zero temperatures.Comment: 12 pages, 3 figure
Quantum spin Hall effect and spin-charge separation in a kagome lattice
A two-dimensional kagome lattice is theoretically investigated within a
simple tight-binding model, which includes the nearest neighbor hopping term
and the intrinsic spin-orbit interaction between the next nearest neighbors. By
using the topological winding properties of the spin-edge states on the
complex-energy Riemann surface, the spin Hall conductance is obtained to be
quantized as () in insulating phases. This result keeps
consistent with the numerical linear-response calculation and the
\textbf{Z} topological invariance analysis. When the sample boundaries
are connected in twist, by which two defects with flux are introduced, we
obtain the spin-charge separated solitons at 1/3 (or 2/3) filling.Comment: 13 NJP pages, 7 figure
Geometry of expanding absolutely continuous invariant measures and the liftability problem
We show that for a large class of maps on manifolds of arbitrary finite
dimension, the existence of a Gibbs-Markov-Young structure (with Lebesgue as
the reference measure) is a necessary as well as sufficient condition for the
existence of an invariant probability measure which is absolutely continuous
measure (with respect to Lebesgue) and for which all Lyapunov exponents are
positive.Comment: 21 pages; final versio
Delocalization of slowly damped eigenmodes on Anosov manifolds
We look at the properties of high frequency eigenmodes for the damped wave
equation on a compact manifold with an Anosov geodesic flow. We study
eigenmodes with spectral parameters which are asymptotically close enough to
the real axis. We prove that such modes cannot be completely localized on
subsets satisfying a condition of negative topological pressure. As an
application, one can deduce the existence of a "strip" of logarithmic size
without eigenvalues below the real axis under this dynamical assumption on the
set of undamped trajectories.Comment: 28 pages; compared with version 1, minor modifications, add two
reference
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