448 research outputs found
Trapping in the random conductance model
We consider random walks on among nearest-neighbor random conductances
which are i.i.d., positive, bounded uniformly from above but whose support
extends all the way to zero. Our focus is on the detailed properties of the
paths of the random walk conditioned to return back to the starting point at
time . We show that in the situations when the heat kernel exhibits
subdiffusive decay --- which is known to occur in dimensions --- the
walk gets trapped for a time of order in a small spatial region. This shows
that the strategy used earlier to infer subdiffusive lower bounds on the heat
kernel in specific examples is in fact dominant. In addition, we settle a
conjecture concerning the worst possible subdiffusive decay in four dimensions.Comment: 21 pages, version to appear in J. Statist. Phy
Mean-field driven first-order phase transitions in systems with long-range interactions
We consider a class of spin systems on with vector valued spins
(\bS_x) that interact via the pair-potentials J_{x,y} \bS_x\cdot\bS_y. The
interactions are generally spread-out in the sense that the 's exhibit
either exponential or power-law fall-off. Under the technical condition of
reflection positivity and for sufficiently spread out interactions, we prove
that the model exhibits a first-order phase transition whenever the associated
mean-field theory signals such a transition. As a consequence, e.g., in
dimensions , we can finally provide examples of the 3-state Potts model
with spread-out, exponentially decaying interactions, which undergoes a
first-order phase transition as the temperature varies. Similar transitions are
established in dimensions for power-law decaying interactions and in
high dimensions for next-nearest neighbor couplings. In addition, we also
investigate the limit of infinitely spread-out interactions. Specifically, we
show that once the mean-field theory is in a unique ``state,'' then in any
sequence of translation-invariant Gibbs states various observables converge to
their mean-field values and the states themselves converge to a product
measure.Comment: 57 pages; uses a (modified) jstatphys class fil
Optimal designs for rational function regression
We consider optimal non-sequential designs for a large class of (linear and
nonlinear) regression models involving polynomials and rational functions with
heteroscedastic noise also given by a polynomial or rational weight function.
The proposed method treats D-, E-, A-, and -optimal designs in a
unified manner, and generates a polynomial whose zeros are the support points
of the optimal approximate design, generalizing a number of previously known
results of the same flavor. The method is based on a mathematical optimization
model that can incorporate various criteria of optimality and can be solved
efficiently by well established numerical optimization methods. In contrast to
previous optimization-based methods proposed for similar design problems, it
also has theoretical guarantee of its algorithmic efficiency; in fact, the
running times of all numerical examples considered in the paper are negligible.
The stability of the method is demonstrated in an example involving high degree
polynomials. After discussing linear models, applications for finding locally
optimal designs for nonlinear regression models involving rational functions
are presented, then extensions to robust regression designs, and trigonometric
regression are shown. As a corollary, an upper bound on the size of the support
set of the minimally-supported optimal designs is also found. The method is of
considerable practical importance, with the potential for instance to impact
design software development. Further study of the optimality conditions of the
main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory
and additional example
Superconductivity and charge carrier localization in ultrathin bilayers
/ (LSCO15/LCO) bilayers
with a precisely controlled thickness of N unit cells (UCs) of the former and M
UCs of the latter ([LSCO15\_N/LCO\_M]) were grown on (001)-oriented {\slao}
(SLAO) substrates with pulsed laser deposition (PLD). X-ray diffraction and
reciprocal space map (RSM) studies confirmed the epitaxial growth of the
bilayers and showed that a [LSCO15\_2/LCO\_2] bilayer is fully strained,
whereas a [LSCO15\_2/LCO\_7] bilayer is already partially relaxed. The
\textit{in situ} monitoring of the growth with reflection high energy electron
diffraction (RHEED) revealed that the gas environment during deposition has a
surprisingly strong effect on the growth mode and thus on the amount of
disorder in the first UC of LSCO15 (or the first two monolayers of LSCO15
containing one plane each). For samples grown in pure
gas (growth type-B), the first LSCO15 UC next to the SLAO
substrate is strongly disordered. This disorder is strongly reduced if the
growth is performed in a mixture of and gas
(growth type-A). Electric transport measurements confirmed that the first UC of
LSCO15 next to the SLAO substrate is highly resistive and shows no sign of
superconductivity for growth type-B, whereas it is superconducting for growth
type-A. Furthermore, we found, rather surprisingly, that the conductivity of
the LSCO15 UC next to the LCO capping layer strongly depends on the thickness
of the latter. A LCO capping layer with 7~UCs leads to a strong localization of
the charge carriers in the adjacent LSCO15 UC and suppresses superconductivity.
The magneto-transport data suggest a similarity with the case of weakly hole
doped LSCO single crystals that are in a so-called {"{cluster-spin-glass
state}"
Quantum spin systems at positive temperature
We develop a novel approach to phase transitions in quantum spin models based
on a relation to their classical counterparts. Explicitly, we show that
whenever chessboard estimates can be used to prove a phase transition in the
classical model, the corresponding quantum model will have a similar phase
transition, provided the inverse temperature and the magnitude of the
quantum spins \CalS satisfy \beta\ll\sqrt\CalS. From the quantum system we
require that it is reflection positive and that it has a meaningful classical
limit; the core technical estimate may be described as an extension of the
Berezin-Lieb inequalities down to the level of matrix elements. The general
theory is applied to prove phase transitions in various quantum spin systems
with \CalS\gg1. The most notable examples are the quantum orbital-compass
model on and the quantum 120-degree model on which are shown to
exhibit symmetry breaking at low-temperatures despite the infinite degeneracy
of their (classical) ground state.Comment: 47 pages, version to appear in CMP (style files included
Pulsed laser deposition growth of heteroepitaxial YBa2Cu3O7/La0.67Ca0.33MnO3 superlattices on NdGaO3 and Sr0.7La0.3Al0.65Ta0.35O3 substrates
Heteroepitaxial superlattices of [YBa2Cu3O7(n)/ La0.67Ca0.33MnO3(m)]x, where
n and m are the number of YBCO and LCMO monolayers and x the number of bilayer
repetitions, have been grown with pulsed laser deposition on NdGaO3 (110) and
Sr0.7La0.3Al0.65Ta0.35O3 (LSAT) (001). These substrates are well lattice
matched with YBCO and LCMO and, unlike the commonly used SrTiO3, they do not
give rise to complex and uncontrolled strain effects due to structural
transitions at low temperature. The growth dynamics and the structure have been
studied in-situ with reflection high energy electron diffraction (RHEED) and
ex-situ with scanning transmission electron microscopy (STEM), x-ray
diffraction, and neutron reflectometry. The individual layers are found to be
flat and continuous over long lateral distances with sharp and coherent
interfaces and with a well-defined thickness of the individual layer. The only
visible defects are antiphase boundaries in the YBCO layers that originate from
perovskite unit cell height steps at the interfaces with the LCMO layers. We
also find that the first YBCO monolayer at the interface with LCMO has an
unusual growth dynamics and is lacking the CuO chain layer while the subsequent
YBCO layers have the regular Y-123 structure. Accordingly, the CuO2 bilayers at
both the LCMO/YBCO and the YBCO/LCMO interfaces are lacking one of their
neighboring CuO chain layers and thus half of their hole doping reservoir.
Nevertheless, from electric transport measurements on asuperlattice with n=2 we
obtain evidence that the interfacial CuO2 bilayers remain conducting and even
exhibit the onset of a superconducting transition at very low temperature.
Finally, we show from dc magnetization and neutron reflectometry measurements
that the LCMO layers are strongly ferromagnetic
A new quantum fluid at high magnetic fields in the marginal charge-density-wave system -(BEDT-TTF)Hg(SCN) (where ~K and Rb)
Single crystals of the organic charge-transfer salts
-(BEDT-TTF)Hg(SCN) have been studied using Hall-potential
measurements (K) and magnetization experiments ( = K, Rb). The data show
that two types of screening currents occur within the high-field,
low-temperature CDW phases of these salts in response to time-dependent
magnetic fields. The first, which gives rise to the induced Hall potential, is
a free current (), present at the surface of the sample.
The time constant for the decay of these currents is much longer than that
expected from the sample resistivity. The second component of the current
appears to be magnetic (), in that it is a microscopic,
quasi-orbital effect; it is evenly distributed within the bulk of the sample
upon saturation. To explain these data, we propose a simple model invoking a
new type of quantum fluid comprising a CDW coexisting with a two-dimensional
Fermi-surface pocket which describes the two types of current. The model and
data are able to account for the body of previous experimental data which had
generated apparently contradictory interpretations in terms of the quantum Hall
effect or superconductivity.Comment: 13 pages, 11 figure
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