396 research outputs found
Ground state properties of antiferromagnetic Heisenberg spin rings
Exact ground state properties of antiferromagnetic Heisenberg spin rings with
isotropic next neighbour interaction are presented for various numbers of spin
sites and spin quantum numbers. Earlier work by Peierls, Marshall, Lieb,
Schultz and Mattis focused on bipartite lattices and is not applicable to rings
with an odd number of spins. With the help of exact diagonalization methods we
find a more general systematic behaviour which for instance relates the number
of spin sites and the individual spin quantum numbers to the degeneracy of the
ground state. These numerical findings all comply with rigorous proofs in the
cases where a general analysis could be carried out. Therefore it can be
plausibly conjectured that the ascertained properties hold for ground states of
arbitrary antiferromagnetic Heisenberg spin rings.Comment: 13 pages, 5 figures, uses epsfig.sty, submitted to Phys. Rev. B. More
information at http://www.physik.uni-osnabrueck.de/makrosysteme
Proton Spin Relaxation Induced by Quantum Tunneling in Fe8 Molecular Nanomagnet
The spin-lattice relaxation rate and NMR spectra of H in
single crystal molecular magnets of Fe8 have been measured down to 15 mK. The
relaxation rate shows a strong temperature dependence down to 400
mK. The relaxation is well explained in terms of the thermal transition of the
iron state between the discreet energy levels of the total spin S=10. The
relaxation time becomes temperature independent below 300 mK and is
longer than 100 s. In this temperature region stepwise recovery of the
H-NMR signal after saturation was observed depending on the return field of
the sweep field. This phenomenon is attributed to resonant quantum tunneling at
the fields where levels cross and is discussed in terms of the Landau-Zener
transition.Comment: 13 pages, 5 figure
Heisenberg exchange parameters of molecular magnets from the high-temperature susceptibility expansion
We provide exact analytical expressions for the magnetic susceptibility
function in the high temperature expansion for finite Heisenberg spin systems
with an arbitrary coupling matrix, arbitrary single-spin quantum number, and
arbitrary number of spins. The results can be used to determine unknown
exchange parameters from zero-field magnetic susceptibility measurements
without diagonalizing the system Hamiltonian. We demonstrate the possibility of
reconstructing the exchange parameters from simulated data for two specific
model systems. We examine the accuracy and stability of the proposed method.Comment: 13 pages, 7 figures, submitted to Phys. Rev.
Aeroacoustics research in Europe: The CEAS-ASC report on 2020 & 2021 highlights
The Council of European Aerospace Societies (CEAS) Aeroacoustics Specialists Committee (ASC) supports and promotes the interests of the scientific and industrial aeroacoustics community on a European scale and European aeronautics activities internationally. In this context, “aeroacoustics” encompasses all aerospace acoustics and related areas. Each year the committee highlights some of the research and development projects in Europe.
Due the effects of the Covid 19 pandemic it was not possible to publish an edition in 2021 and so this paper is a report on highlights of aeroacoustics research in Europe in both 2020 and 2021, compiled from information provided to the ASC of the CEAS. In addition, during 2020 and 2021, a number of research programmes involving aeroacoustics were funded by the European Commission. Some of the highlights from these programmes are also summarized in this article.
Enquiries concerning all contributions should be addressed to the authors who are given at the end of each subsection
High frequency resonant experiments in Fe molecular clusters
Precise resonant experiments on Fe magnetic clusters have been
conducted down to 1.2 K at various tranverse magnetic fields, using a
cylindrical resonator cavity with 40 different frequencies between 37 GHz and
110 GHz. All the observed resonances for both single crystal and oriented
powder, have been fitted by the eigenstates of the hamiltonian . We have identified the
resonances corresponding to the coherent quantum oscillations for different
orientations of spin S = 10.Comment: to appear in Phys.Rev. B (August 2000
Insights into the mechanism for gold catalysis: behaviour of gold(i) amide complexes in solution
We report the synthesis and activity of new mononuclear and dinuclear gold amide complexes . The dinuclear complexes and were characterised by single crystal X-ray analysis. We also report solution NMR and freezing point depression experiments to rationalise their behaviour in solution and question the de-ligation process invoked in gold catalysis
CSIDH on the surface
For primes p≡3mod4, we show that setting up CSIDH on the surface, i.e., using supersingular elliptic curves with endomorphism ring Z[(1+−p−−−√)/2], amounts to just a few sign switches in the underlying arithmetic. If p≡7mod8 then horizontal 2-isogenies can be used to help compute the class group action. The formulas we derive for these 2-isogenies are very efficient (they basically amount to a single exponentiation in Fp) and allow for a noticeable speed-up, e.g., our resulting CSURF-512 protocol runs about 5.68% faster than CSIDH-512. This improvement is completely orthogonal to all previous speed-ups, constant-time measures and construction of cryptographic primitives that have appeared in the literature so far. At the same time, moving to the surface gets rid of the redundant factor Z3 of the acting ideal-class group, which is present in the case of CSIDH and offers no extra security
Characterization of the S = 9 excited state in Fe8Br8 by Electron Paramagnetic Resonance
High Frequency electron paramagnetic resonance has been used to observe the
magnetic dipole, M = 1, transitions in the excited
state of the single molecule magnet FeBr. A Boltzmann analysis of the
measured intensities locates it at 24 2 K above the ground
state, while the line positions yield its magnetic parameters D = -0.27 K, E =
0.05 K, and B = -1.3 10 K. D is thus smaller by 8%
and E larger by 7% than for . The anisotropy barrier for is
estimated as 22 K,which is 25% smaller than that for (29 K). These
data also help assign the spin exchange constants(J's) and thus provide a basis
for improved electronic structure calculations of FeBr.Comment: 7 pages, Figs included in text, submitted to PR
Uniform bounds on complexity and transfer of global properties of Nash functions
We show that the complexity of semialgebraic sets and mappings can be used to parametrize Nash sets and mappings by Nash families. From this we deduce uniform bounds on the complexity of Nash functions that lead to first-order descriptions of many properties of Nash functions and a good behaviour under real closed field extension (e.g. primary decomposition). As a distinguished application, we derive the solution of the extension and global equations problems over arbitrary real closed fields, in particular over the field of real algebraic numbers. This last fact and a technique of change of base are used to prove that the Artin-Mazur description holds for abstract Nash functions on the real spectrum of any commutative ring, and solve extension and global equations in that abstract setting. To complete the view, we prove the idempotency of the real spectrum and an abstract version of the separation problem. We also discuss the conditions for the rings of abstract Nash functions to be noetherian
Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
The determination of the energy spectra of small spin systems as for instance
given by magnetic molecules is a demanding numerical problem. In this work we
review numerical approaches to diagonalize the Heisenberg Hamiltonian that
employ symmetries; in particular we focus on the spin-rotational symmetry SU(2)
in combination with point-group symmetries. With these methods one is able to
block-diagonalize the Hamiltonian and thus to treat spin systems of
unprecedented size. In addition it provides a spectroscopic labeling by
irreducible representations that is helpful when interpreting transitions
induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance
(NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the
reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure
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