767 research outputs found
Diagonalization of a bosonic quadratic form using CCM: Application on a system with two interpenetrating square lattice antiferromagnets
While the diagonalization of a quadratic bosonic form can always be done
using a Bogoliubov transformation, the practical implementation for systems
with a large number of different bosons is a tedious analytical task. Here we
use the coupled cluster method (CCM) to exactly diagonalise such complicated
quadratic forms. This yields to a straightforward algorithm which can easily be
implemented using computer algebra even for a large number of different bosons.
We apply this method on a Heisenberg system with two interpenetrating square
lattice antiferromagnets, which is a model for the quasi 2D antiferromagnet
Ba_2Cu_3O_4Cl_2. Using a four-magnon spin wave approximation we get a
complicated Hamiltonian with four different bosons, which is treated with CCM.
Results are presented for magnetic ground state correlations.Comment: 4 pages, 2 Postscript figures, to be published in acta physica
polonica A (European Conference 'Physics of Magnetism 99'
Stochastic Shell Models driven by a multiplicative fractional Brownian--motion
We prove existence and uniqueness of the solution of a stochastic
shell--model. The equation is driven by an infinite dimensional fractional
Brownian--motion with Hurst--parameter , and contains a
non--trivial coefficient in front of the noise which satisfies special
regularity conditions. The appearing stochastic integrals are defined in a
fractional sense. First, we prove the existence and uniqueness of variational
solutions to approximating equations driven by piecewise linear continuous
noise, for which we are able to derive important uniform estimates in some
functional spaces. Then, thanks to a compactness argument and these estimates,
we prove that these variational solutions converge to a limit solution, which
turns out to be the unique pathwise mild solution associated to the
shell--model with fractional noise as driving process.Comment: 23 page
Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients
In this paper we study the longtime dynamics of mild solutions to retarded
stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a
preparation for this purpose we have to show the existence and uniqueness of a
cocycle solution of such an equation. We do not assume that the noise is given
in additive form or that it is a very simple multiplicative noise. However, we
need some smoothing property for the coefficient in front of the noise. The
main idea of this paper consists of expressing the stochastic integral in terms
of non-stochastic integrals and the noisy path by using an integration by
parts. This latter term causes that in a first moment only a local mild
solution can be obtained, since in order to apply the Banach fixed point
theorem it is crucial to have the H\"older norm of the noisy path to be
sufficiently small. Later, by using appropriate stopping times, we shall derive
the existence and uniqueness of a global mild solution. Furthermore, the
asymptotic behavior is investigated by using the {\it Random Dynamical Systems
theory}. In particular, we shall show that the global mild solution generates a
random dynamical system that, under an appropriate smallness condition for the
time lag, have associated a random attractor
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