43,752 research outputs found
Frustration effects in magnetic molecules
By means of exact diagonalization we study the ground-state and the
low-temperature physics of the Heisenberg antiferromagnet on the cuboctahedron
and the icosidodecahedron. Both are frustrated magnetic polytopes and
correspond to the arrangement of magnetic atoms in the magnetic molecules
Cu12La8 and Mo72Fe30. The interplay of strong quantum fluctuations and
frustration influences the ground state spin correlations drastically and leads
to an interesting magnetization process at low temperatures. Furthermore the
frustration yields low-lying non-magnetic excitations resulting in an extra
low-temperature peak in the specific heat.Comment: 4 pages, 7 figure
Trip-Based Public Transit Routing
We study the problem of computing all Pareto-optimal journeys in a public
transit network regarding the two criteria of arrival time and number of
transfers taken. We take a novel approach, focusing on trips and transfers
between them, allowing fine-grained modeling. Our experiments on the
metropolitan network of London show that the algorithm computes full 24-hour
profiles in 70 ms after a preprocessing phase of 30 s, allowing fast queries in
dynamic scenarios.Comment: Minor corrections, no substantial changes. To be presented at ESA
201
Solitary-wave description of condensate micro-motion in a time-averaged orbiting potential trap
We present a detailed theoretical analysis of micro-motion in a time-averaged
orbiting potential trap. Our treatment is based on the Gross-Pitaevskii
equation, with the full time dependent behaviour of the trap systematically
approximated to reduce the trapping potential to its dominant terms. We show
that within some well specified approximations, the dynamic trap has
solitary-wave solutions, and we identify a moving frame of reference which
provides the most natural description of the system. In that frame eigenstates
of the time-averaged orbiting potential trap can be found, all of which must be
solitary-wave solutions with identical, circular centre of mass motion in the
lab frame. The validity regime for our treatment is carefully defined, and is
shown to be satisfied by existing experimental systems.Comment: 12 pages, 2 figure
Asymptotics of relative heat traces and determinants on open surfaces of finite area
The goal of this paper is to prove that on surfaces with asymptotically cusp
ends the relative determinant of pairs of Laplace operators is well defined. We
consider a surface with cusps (M,g) and a metric h on the surface that is a
conformal transformation of the initial metric g. We prove the existence of the
relative determinant of the pair under suitable
conditions on the conformal factor. The core of the paper is the proof of the
existence of an asymptotic expansion of the relative heat trace for small
times. We find the decay of the conformal factor at infinity for which this
asymptotic expansion exists and the relative determinant is defined. Following
the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of
determinants on compact surfaces, we prove Polyakov's formula for the relative
determinant and discuss the extremal problem inside a conformal class. We
discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51
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