18,001 research outputs found
On the mechanism of action of the cytostatic drug anguidine and of the immunosuppressive agent ovalicin, two sesquiterpenes from fungi
Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method
We present a method for the direct calculation of the spin stiffness by means
of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on
the square, the triangular and the cubic lattices we calculate the stiffness in
high orders of approximation. For the square and the cubic lattices our results
are in very good agreement with the best results available in the literature.
For the triangular lattice our result is more precise than any other result
obtained so far by other approximate method.Comment: 5 pages, 2 figure
Nonlinear projective filtering in a data stream
We introduce a modified algorithm to perform nonlinear filtering of a time
series by locally linear phase space projections. Unlike previous
implementations, the algorithm can be used not only for a posteriori processing
but includes the possibility to perform real time filtering in a data stream.
The data base that represents the phase space structure generated by the data
is updated dynamically. This also allows filtering of non-stationary signals
and dynamic parameter adjustment. We discuss exemplary applications, including
the real time extraction of the fetal electrocardiogram from abdominal
recordings.Comment: 8 page
Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet
We consider the zero-temperature properties of the spin-half two-dimensional
Shastry-Sutherland antiferromagnet by using a high-order coupled cluster method
(CCM) treatment. We find that this model demonstrates various groundstate
phases (N\'{e}el, magnetically disordered, orthogonal dimer), and we make
predictions for the positions of the phase transition points. In particular, we
find that orthogonal-dimer state becomes the groundstate at . For the critical point where the semi-classical N\'eel
order disappears we obtain a significantly lower value than ,
namely, in the range . We therefore conclude that
an intermediate phase exists between the \Neel and the dimer phases. An
analysis of the energy of a competing spiral phase yields clear evidence that
the spiral phase does not become the groundstate for any value of . The
intermediate phase is therefore magnetically disordered but may exhibit
plaquette or columnar dimer ordering.Comment: 6 pages, 5 figure
The sawtooth chain: From Heisenberg spins to Hubbard electrons
We report on recent studies of the spin-half Heisenberg and the Hubbard model
on the sawtooth chain. For both models we construct a class of exact
eigenstates which are localized due to the frustrating geometry of the lattice
for a certain relation of the exchange (hopping) integrals. Although these
eigenstates differ in details for the two models because of the different
statistics, they share some characteristic features. The localized eigenstates
are highly degenerate and become ground states in high magnetic fields
(Heisenberg model) or at certain electron fillings (Hubbard model),
respectively. They may dominate the low-temperature thermodynamics and lead to
an extra low-temperature maximum in the specific heat. The ground-state
degeneracy can be calculated exactly by a mapping of the manifold of localized
ground states onto a classical hard-dimer problem, and explicit expressions for
thermodynamic quantities can be derived which are valid at low temperatures
near the saturation field for the Heisenberg model or around a certain value of
the chemical potential for the Hubbard model, respectively.Comment: 16 pages, 6 figure, the paper is based on an invited talk on the XXXI
International Workshop on Condensed Matter Theories, Bangkok, Dec 2007;
notation of x-axis in Fig.6 corrected, references update
Improved bounds for the crossing numbers of K_m,n and K_n
It has been long--conjectured that the crossing number cr(K_m,n) of the
complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):=
floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing
conjecture states that the crossing number cr(K_n) of the complete graph K_n
equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In
this paper we show the following improved bounds on the asymptotic ratios of
these crossing numbers and their conjectured values:
(i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1);
(ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and
(iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83.
The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8,
respectively. These improved bounds are obtained as a consequence of the new
bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for
cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to
set up a quadratic program on 6! variables whose minimum p satisfies
cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic
optimization techniques combined with a bit of invariant theory of permutation
groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure
Effect of anisotropy on the ground-state magnetic ordering of the spin-one quantum -- model on the square lattice
We study the zero-temperature phase diagram of the
-- Heisenberg model for spin-1 particles on an
infinite square lattice interacting via nearest-neighbour () and
next-nearest-neighbour () bonds. Both bonds have the same -type
anisotropy in spin space. The effects on the quasiclassical N\'{e}el-ordered
and collinear stripe-ordered states of varying the anisotropy parameter
is investigated using the coupled cluster method carried out to high
orders. By contrast with the spin-1/2 case studied previously, we predict no
intermediate disordered phase between the N\'{e}el and collinear stripe phases,
for any value of the frustration , for either the -aligned () or -planar-aligned () states. The quantum phase
transition is determined to be first-order for all values of and
. The position of the phase boundary is determined
accurately. It is observed to deviate most from its classical position (for all values of ) at the Heisenberg isotropic point
(), where . By contrast, at the XY
isotropic point (), we find . In the
Ising limit () as expected.Comment: 20 pages, 5 figure
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