2,503 research outputs found
Supercritical holes for the doubling map
For a map and an open connected set ( a hole) we
define to be the set of points in whose -orbit avoids
. We say that a hole is supercritical if (i) for any hole such
that the set is either empty or contains
only fixed points of ; (ii) for any hole such that \barH\subset H_0
the Hausdorff dimension of is positive.
The purpose of this note to completely characterize all supercritical holes
for the doubling map .Comment: This is a new version, where a full characterization of supercritical
holes for the doubling map is obtaine
Anomalous Pressure Dependence of Kadowaki-Woods ratio and Crystal Field Effects in Mixed-valence YbInCu4
The mixed-valence (MV) compound YbInCu4 was investigated by electrical
resistivity and ac specific heat at low temperatures and high pressures. At
atmospheric pressure, its Kadowaki-Woods (KW) ratio, A/\gamma ^2, is 16 times
smaller than the universal value R_{KW}(=1.0 x 10^-5 \mu \Omega cm mol^2 K^2
mJ^-2), but sharply increases to 16.5R_{KW} at 27 kbar. The pressure-induced
change in the KW ratio and deviation from R_{KW} are analyzed in terms of the
change in f-orbital degeneracy N and carrier density n. This analysis is
further supported by a dramatic change in residual resistivity \rho_0 near 25
kbar, where \rho_0 jumps by a factor of 7.Comment: 4pages, 3figure
Two-channel point-contact tunneling theory of superconductors
We introduce a two-channel tunneling model to generalize the widely used BTK
theory of point-contact conductance between a normal metal contact and
superconductor. Tunneling of electrons can occur via localized surface states
or directly, resulting in a Fano resonance in the differential conductance
. We present an analysis of within the two-channel model when
applied to soft point-contacts between normal metallic silver particles and
prototypical heavy-fermion superconductors CeCoIn and CeRhIn at high
pressures. In the normal state the Fano line shape of the measured is well
described by a model with two tunneling channels and a large
temperature-independent background conductance. In the superconducting state a
strongly suppressed Andreev reflection signal is explained by the presence of
the background conductance. We report Andreev signal in CeCoIn consistent
with standard -wave pairing, assuming an equal mixture of
tunneling into [100] and [110] crystallographic interfaces. Whereas in
CeRhIn at 1.8 and 2.0 GPa the signal is described by a -wave
gap with reduced nodal region, i.e., increased slope of the gap opening on the
Fermi surface. A possibility is that the shape of the high-pressure Andreev
signal is affected by the proximity of a line of quantum critical points that
extends from 1.75 to 2.3 GPa, which is not accounted for in our description of
the heavy-fermion superconductor.Comment: 13 pages, 13 figure
Two Superconducting Phases in CeRh_1-xIr_xIn_5
Pressure studies of CeRh_1-xIr_xIn_5 indicate two superconducting phases as a
function of x, one with T_c >= 2 K for x < 0.9 and the other with T_c < 1.2 K
for x > 0.9. The higher T_c phase, phase-1, emerges in proximity to an
antiferromagnetic quantum-critical point; whereas, Cooper pairing in the lower
T_c phase-2 is inferred to arise from fluctuations of a yet to be found
magnetic state. The T-x-P phase diagram of CeRh_1-xIr_xIn_5, though
qualitatively similar, is distinctly different from that of
CeCu_2(Si_1-xGe_x)_2.Comment: 5 pages, 3 figure
Pressure effects on the heavy-fermion antiferromagnet CeAuSb2
The f-electron compound CeAuSb2, which crystallizes in the ZrCuSi2-type
tetragonal structure, orders antiferromagnetically between 5 and 6.8 K, where
the antiferromagnetic transition temperature T_N depends on the occupancy of
the Au site. Here we report the electrical resistivity and heat capacity of a
high-quality crystal CeAuSb2 with T_N of 6.8 K, the highest for this compound.
The magnetic transition temperature is initially suppressed with pressure, but
is intercepted by a new magnetic state above 2.1 GPa. The new phase shows a
dome shape with pressure and coexists with another phase at pressures higher
than 4.7 GPa. The electrical resistivity shows a T^2 Fermi liquids behavior in
the complex magnetic state, and the residual resistivity and the T^2
resistivity coefficient increases with pressure, suggesting the possibility of
a magnetic quantum critical point at a higher pressure.Comment: 5 pages, 5 firure
Combinatorics of linear iterated function systems with overlaps
Let be points in , and let
be a one-parameter family of similitudes of : where
is our parameter. Then, as is well known, there exists a
unique self-similar attractor satisfying
. Each has
at least one address , i.e.,
.
We show that for sufficiently close to 1, each has different
addresses. If is not too close to 1, then we can still have an
overlap, but there exist 's which have a unique address. However, we
prove that almost every has addresses,
provided contains no holes and at least one proper overlap. We
apply these results to the case of expansions with deleted digits.
Furthermore, we give sharp sufficient conditions for the Open Set Condition
to fail and for the attractor to have no holes.
These results are generalisations of the corresponding one-dimensional
results, however most proofs are different.Comment: Accepted for publication in Nonlinearit
Presure-Induced Superconducting State of Antiferromagnetic CaFeAs
The antiferromagnet CaFeAs does not become superconducting when
subject to ideal hydrostatic pressure conditions, where crystallographic and
magnetic states also are well defined. By measuring electrical resistivity and
magnetic susceptibility under quasi-hydrostatic pressure, however, we find that
a substantial volume fraction of the sample is superconducting in a narrow
pressure range where collapsed tetragonal and orthorhombic structures coexist.
At higher pressures, the collapsed tetragonal structure is stabilized, with the
boundary between this structure and the phase of coexisting structures strongly
dependent on pressure history. Fluctuations in magnetic degrees of freedom in
the phase of coexisting structures appear to be important for
superconductivity.Comment: revised (6 pages, 5 figures) - includes additional experimental
result
- β¦