2,483 research outputs found
Spectral bounds for the Hellmann potential
The method of potential envelopes is used to analyse the bound state spectrum
of the Schroedinger Hamiltonian H=-\Delta+V(r), where the Hellmann potential is
given by V(r) = -A/r + Be^{-Cr}/r, A and C are positive, and B can be positive
or negative. We established simple formulas yielding upper and lower bounds for
all the energy eigenvalues.Comment: 9 pages, 2 figures, typos correcte
SWEEPFINDER2: Increased sensitivity, robustness, and flexibility
SweepFinder is a popular program that implements a powerful likelihood-based
method for detecting recent positive selection, or selective sweeps. Here, we
present SweepFinder2, an extension of SweepFinder with increased sensitivity
and robustness to the confounding effects of mutation rate variation and
background selection, as well as increased flexibility that enables the user to
examine genomic regions in greater detail and to specify a fixed distance
between test sites. Moreover, SweepFinder2 enables the use of invariant sites
for sweep detection, increasing both its power and precision relative to
SweepFinder
A Bell-Evans-Polanyi principle for molecular dynamics trajectories and its implications for global optimization
The Bell-Evans-Polanyi principle that is valid for a chemical reaction that
proceeds along the reaction coordinate over the transition state is extended to
molecular dynamics trajectories that in general do not cross the dividing
surface between the initial and the final local minima at the exact transition
state. Our molecular dynamics Bell-Evans-Polanyi principle states that low
energy molecular dynamics trajectories are more likely to lead into the basin
of attraction of a low energy local minimum than high energy trajectories. In
the context of global optimization schemes based on molecular dynamics our
molecular dynamics Bell-Evans-Polanyi principle implies that using low energy
trajectories one needs to visit a smaller number of distinguishable local
minima before finding the global minimum than when using high energy
trajectories
Stability in the instantaneous Bethe-Salpeter formalism: harmonic-oscillator reduced Salpeter equation
A popular three-dimensional reduction of the Bethe-Salpeter formalism for the
description of bound states in quantum field theory is the Salpeter equation,
derived by assuming both instantaneous interactions and free propagation of all
bound-state constituents. Numerical (variational) studies of the Salpeter
equation with confining interaction, however, observed specific instabilities
of the solutions, likely related to the Klein paradox and rendering (part of
the) bound states unstable. An analytic investigation of this problem by a
comprehensive spectral analysis is feasible for the reduced Salpeter equation
with only harmonic-oscillator confining interactions. There we are able to
prove rigorously that the bound-state solutions correspond to real discrete
energy spectra bounded from below and are thus free of any instabilities.Comment: 23 pages, 3 figures, extended conclusions, version to appear in Phys.
Rev.
Quantum phase transitions in photonic cavities with two-level systems
Systems of coupled photonic cavities have been predicted to exhibit quantum
phase transitions by analogy with the Hubbard model. To this end, we have
studied topologies of few (up to six) photonic cavities each containing a
single two-level system. Quantum phase space diagrams are produced for these
systems, and compared to mean-field results. We also consider finite effective
temperature, and compare this to the notion of disorder. We find the extent of
the Mott lobes shrink analogously to the conventional Bose-Hubbard model.Comment: 11 pages, 11 figures, updated typo
On the Expansions in Spin Foam Cosmology
We discuss the expansions used in spin foam cosmology. We point out that
already at the one vertex level arbitrarily complicated amplitudes contribute,
and discuss the geometric asymptotics of the five simplest ones. We discuss
what type of consistency conditions would be required to control the expansion.
We show that the factorisation of the amplitude originally considered is best
interpreted in topological terms. We then consider the next higher term in the
graph expansion. We demonstrate the tension between the truncation to small
graphs and going to the homogeneous sector, and conclude that it is necessary
to truncate the dynamics as well.Comment: 17 pages, 4 figures, published versio
Linking entanglement and quantum phase transitions via density functional theory
Density functional theory (DFT) is shown to provide a novel conceptual and
computational framework for entanglement in interacting many-body quantum
systems. DFT can, in particular, shed light on the intriguing relationship
between quantum phase transitions and entanglement. We use DFT concepts to
express entanglement measures in terms of the first or second derivative of the
ground state energy. We illustrate the versatility of the DFT approach via a
variety of analytically solvable models. As a further application we discuss
entanglement and quantum phase transitions in the case of mean field
approximations for realistic models of many-body systems.Comment: 6 pages, 2 figure
New Method to Calculate Electrical Forces Acting on a Sphere in an Electrorheological Fluid
We describe a method to calculate the electrical force acting on a sphere in
a suspension of dielectric spheres in a host with a different dielectric
constant, under the assumption that a spatially uniform electric field is
applied. The method uses a spectral representation for the total electrostatic
energy of the composite. The force is expressed as a certain gradient of this
energy, which can be expressed in a closed analytic form rather than evaluated
as a numerical derivative. The method is applicable even when both the spheres
and the host have frequency-dependent dielectric functions and nonzero
conductivities, provided the system is in the quasistatic regime. In principle,
it includes all multipolar contributions to the force, and it can be used to
calculate multi-body as well as pairwise forces. We also present several
numerical examples, including host fluids with finite conductivities. The force
between spheres approaches the dipole-dipole limit, as expected, at large
separations, but departs drastically from that limit when the spheres are
nearly in contact. The force may also change sign as a function of frequency
when the host is a slightly conducting fluid.Comment: 29 pages, 8 figures, Accepted for Publication in Physical Review
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