2,761 research outputs found
Fully quantum mechanical moment of inertia of a mesoscopic ideal Bose gas
The superfluid fraction of an atomic cloud can be defined using the cloud's
response to a rotation of the external potential, i.e. the moment of inertia.
In this paper we derive analytical results for the moment of inertia of a small
number of non-interacting Bosons using the canonical ensemble. The required
symmetrized averages are obtained via a representation of the partition
function by permutation cycles. Our results are useful to discriminate purely
quantum statistical effects from interaction effects in studies of
superfluidity and phase transitions in finite samples.Comment: 6 pages, 1 figures, latest version has an new title and some small
textual change
Output from an atom laser: theory vs. experiment
Atom lasers based on rf-outcoupling can be described by a set of coupled
generalized Gross-Pitaevskii equations (GPE). We compare the theoretical
predictions obtained by numerically integrating the time-dependent GPE of an
effective one-dimensional model with recently measured experimental data for
the F=2 and F=1 states of Rb-87. We conclude that the output of a rf-atom laser
can be well described by this model.Comment: 4 pages, 5 figures, submitted to App. Phys.
Every simple compact semiring is finite
A Hausdorff topological semiring is called simple if every non-zero
continuous homomorphism into another Hausdorff topological semiring is
injective. Classical work by Anzai and Kaplansky implies that any simple
compact ring is finite. We generalize this result by proving that every simple
compact semiring is finite, i.e., every infinite compact semiring admits a
proper non-trivial quotient.Comment: 6 page
Extrapolation-Based Super-Convergent Implicit-Explicit Peer Methods with A-stable Implicit Part
In this paper, we extend the implicit-explicit (IMEX) methods of Peer type
recently developed in [Lang, Hundsdorfer, J. Comp. Phys., 337:203--215, 2017]
to a broader class of two-step methods that allow the construction of
super-convergent IMEX-Peer methods with A-stable implicit part. IMEX schemes
combine the necessary stability of implicit and low computational costs of
explicit methods to efficiently solve systems of ordinary differential
equations with both stiff and non-stiff parts included in the source term. To
construct super-convergent IMEX-Peer methods with favourable stability
properties, we derive necessary and sufficient conditions on the coefficient
matrices and apply an extrapolation approach based on already computed stage
values. Optimised super-convergent IMEX-Peer methods of order s+1 for s=2,3,4
stages are given as result of a search algorithm carefully designed to balance
the size of the stability regions and the extrapolation errors. Numerical
experiments and a comparison to other IMEX-Peer methods are included.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1610.0051
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