18,470 research outputs found
The Tails of the Crossing Probability
The scaling of the tails of the probability of a system to percolate only in
the horizontal direction was investigated numerically for correlated
site-bond percolation model for .We have to demonstrate that the
tails of the crossing probability far from the critical point have shape
where is the correlation
length index, is the probability of a bond to be closed. At
criticality we observe crossover to another scaling . Here is a scaling index describing the
central part of the crossing probability.Comment: 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical
change
Asymptotic Bound-state Model for Feshbach Resonances
We present an Asymptotic Bound-state Model which can be used to accurately
describe all Feshbach resonance positions and widths in a two-body system. With
this model we determine the coupled bound states of a particular two-body
system. The model is based on analytic properties of the two-body Hamiltonian,
and on asymptotic properties of uncoupled bound states in the interaction
potentials. In its most simple version, the only necessary parameters are the
least bound state energies and actual potentials are not used. The complexity
of the model can be stepwise increased by introducing threshold effects,
multiple vibrational levels and additional potential parameters. The model is
extensively tested on the 6Li-40K system and additional calculations on the
40K-87Rb system are presented.Comment: 13 pages, 8 figure
Predicting scattering properties of ultracold atoms: adiabatic accumulated phase method and mass scaling
Ultracold atoms are increasingly used for high precision experiments that can
be utilized to extract accurate scattering properties. This calls for a
stronger need to improve on the accuracy of interatomic potentials, and in
particular the usually rather inaccurate inner-range potentials. A boundary
condition for this inner range can be conveniently given via the accumulated
phase method. However, in this approach one should satisfy two conditions,
which are in principle conflicting, and the validity of these approximations
comes under stress when higher precision is required. We show that a better
compromise between the two is possible by allowing for an adiabatic change of
the hyperfine mixing of singlet and triplet states for interatomic distances
smaller than the separation radius. A mass scaling approach to relate
accumulated phase parameters in a combined analysis of isotopically related
atom pairs is described in detail and its accuracy is estimated, taking into
account both Born-Oppenheimer and WKB breakdown. We demonstrate how numbers of
singlet and triplet bound states follow from the mass scaling.Comment: 14 pages, 9 figure
The potential of the ground state of NaRb
The X state of NaRb was studied by Fourier transform
spectroscopy. An accurate potential energy curve was derived from more than
8800 transitions in isotopomers NaRb and NaRb. This
potential reproduces the experimental observations within their uncertainties
of 0.003 \rcm to 0.007 \rcm. The outer classical turning point of the last
observed energy level (, ) lies at \AA, leading
to a energy of 4.5 \rcm below the ground state asymptote.Comment: 8 pages, 6 figures and 2 table
Exactly solvable model of the 2D electrical double layer
We consider equilibrium statistical mechanics of a simplified model for the
ideal conductor electrode in an interface contact with a classical
semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of
pointlike unit charges in the stability-against-collapse regime of
reduced inverse temperatures . If there is a potential difference
between the bulk interior of the electrolyte and the grounded interface, the
electrolyte region close to the interface (known as the electrical double
layer) carries some nonzero surface charge density. The model is mappable onto
an integrable semi-infinite sine-Gordon theory with Dirichlet boundary
conditions. The exact form-factor and boundary state information gained from
the mapping provide asymptotic forms of the charge and number density profiles
of electrolyte particles at large distances from the interface. The result for
the asymptotic behavior of the induced electric potential, related to the
charge density via the Poisson equation, confirms the validity of the concept
of renormalized charge and the corresponding saturation hypothesis. It is
documented on the non-perturbative result for the asymptotic density profile at
a strictly nonzero that the Debye-H\"uckel limit is a
delicate issue.Comment: 14 page
Rigorous confidence intervals for critical probabilities
We use the method of Balister, Bollobas and Walters to give rigorous 99.9999%
confidence intervals for the critical probabilities for site and bond
percolation on the 11 Archimedean lattices. In our computer calculations, the
emphasis is on simplicity and ease of verification, rather than obtaining the
best possible results. Nevertheless, we obtain intervals of width at most
0.0005 in all cases
Diffusion-controlled generation of a proton-motive force across a biomembrane
Respiration in bacteria involves a sequence of energetically-coupled electron
and proton transfers creating an electrochemical gradient of protons (a
proton-motive force) across the inner bacterial membrane. With a simple kinetic
model we analyze a redox loop mechanism of proton-motive force generation
mediated by a molecular shuttle diffusing inside the membrane. This model,
which includes six electron-binding and two proton-binding sites, reflects the
main features of nitrate respiration in E. coli bacteria. We describe the time
evolution of the proton translocation process. We find that the electron-proton
electrostatic coupling on the shuttle plays a significant role in the process
of energy conversion between electron and proton components. We determine the
conditions where the redox loop mechanism is able to translocate protons
against the transmembrane voltage gradient above 200 mV with a thermodynamic
efficiency of about 37%, in the physiologically important range of temperatures
from 250 to 350 K.Comment: 26 pages, 4 figures. A similar model is used in arXiv:0806.3233 for a
different biological system. Minor changes in the Acknowledgements sectio
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