569 research outputs found
Entanglement and Sources of Magnetic Anisotropy in Radical Pair-Based Avian Magnetoreceptors
One of the principal models of magnetic sensing in migratory birds rests on
the quantum spin-dynamics of transient radical pairs created photochemically in
ocular cryptochrome proteins. We consider here the role of electron spin
entanglement and coherence in determining the sensitivity of a radical
pair-based geomagnetic compass and the origins of the directional response. It
emerges that the anisotropy of radical pairs formed from spin-polarized
molecular triplets could form the basis of a more sensitive compass sensor than
one founded on the conventional hyperfine-anisotropy model. This property
offers new and more flexible opportunities for the design of biologically
inspired magnetic compass sensors
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
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}"
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
Colligative properties of solutions: I. Fixed concentrations
Using the formalism of rigorous statistical mechanics, we study the phenomena
of phase separation and freezing-point depression upon freezing of solutions.
Specifically, we devise an Ising-based model of a solvent-solute system and
show that, in the ensemble with a fixed amount of solute, a macroscopic phase
separation occurs in an interval of values of the chemical potential of the
solvent. The boundaries of the phase separation domain in the phase diagram are
characterized and shown to asymptotically agree with the formulas used in
heuristic analyses of freezing point depression. The limit of infinitesimal
concentrations is described in a subsequent paper.Comment: 28 pages, 1 fig; see also math-ph/0407035 (both to appear in JSP
On the formation/dissolution of equilibrium droplets
We consider liquid-vapor systems in finite volume at parameter
values corresponding to phase coexistence and study droplet formation due to a
fixed excess of particles above the ambient gas density. We identify
a dimensionless parameter and a
\textrm{universal} value \Deltac=\Deltac(d), and show that a droplet of the
dense phase occurs whenever \Delta>\Deltac, while, for \Delta<\Deltac, the
excess is entirely absorbed into the gaseous background. When the droplet first
forms, it comprises a non-trivial, \textrm{universal} fraction of excess
particles. Similar reasoning applies to generic two-phase systems at phase
coexistence including solid/gas--where the ``droplet'' is crystalline--and
polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas
is presented; generalizations are discussed heuristically.Comment: An announcement of a forthcoming rigorous work on the 2D Ising model;
to appear in Europhys. Let
Monte Carlo study of the evaporation/condensation transition on different Ising lattices
In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous
proof for the behavior of the 2D Ising lattice gas, at a finite volume and a
fixed excess \delta M of particles (spins) above the ambient gas density
(spontaneous magnetisation). By identifying a dimensionless parameter \Delta
(\delta M) and a universal constant \Delta_c, they showed in the limit of large
system sizes that for \Delta < \Delta_c the excess is absorbed in the
background (``evaporated'' system), while for \Delta > \Delta_c a droplet of
the dense phase occurs (``condensed'' system).
To check the applicability of the analytical results to much smaller,
practically accessible system sizes, we performed several Monte Carlo
simulations for the 2D Ising model with nearest-neighbour couplings on a square
lattice at fixed magnetisation M. Thereby, we measured the largest minority
droplet, corresponding to the condensed phase, at various system sizes (L=40,
>..., 640). With analytic values for for the spontaneous magnetisation m_0, the
susceptibility \chi and the Wulff interfacial free energy density \tau_W for
the infinite system, we were able to determine \lambda numerically in very good
agreement with the theoretical prediction.
Furthermore, we did simulations for the spin-1/2 Ising model on a triangular
lattice and with next-nearest-neighbour couplings on a square lattice. Again,
finding a very good agreement with the analytic formula, we demonstrate the
universal aspects of the theory with respect to the underlying lattice. For the
case of the next-nearest-neighbour model, where \tau_W is unknown analytically,
we present different methods to obtain it numerically by fitting to the
distribution of the magnetisation density P(m).Comment: 14 pages, 17 figures, 1 tabl
Optimized broad-histogram simulations for strong first-order phase transitions: Droplet transitions in the large-Q Potts model
The numerical simulation of strongly first-order phase transitions has
remained a notoriously difficult problem even for classical systems due to the
exponentially suppressed (thermal) equilibration in the vicinity of such a
transition. In the absence of efficient update techniques, a common approach to
improve equilibration in Monte Carlo simulations is to broaden the sampled
statistical ensemble beyond the bimodal distribution of the canonical ensemble.
Here we show how a recently developed feedback algorithm can systematically
optimize such broad-histogram ensembles and significantly speed up
equilibration in comparison with other extended ensemble techniques such as
flat-histogram, multicanonical or Wang-Landau sampling. As a prototypical
example of a strong first-order transition we simulate the two-dimensional
Potts model with up to Q=250 different states on large systems. The optimized
histogram develops a distinct multipeak structure, thereby resolving entropic
barriers and their associated phase transitions in the phase coexistence region
such as droplet nucleation and annihilation or droplet-strip transitions for
systems with periodic boundary conditions. We characterize the efficiency of
the optimized histogram sampling by measuring round-trip times tau(N,Q) across
the phase transition for samples of size N spins. While we find power-law
scaling of tau vs. N for small Q \lesssim 50 and N \lesssim 40^2, we observe a
crossover to exponential scaling for larger Q. These results demonstrate that
despite the ensemble optimization broad-histogram simulations cannot fully
eliminate the supercritical slowing down at strongly first-order transitions.Comment: 11 pages, 12 figure
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