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 $H\in (1/2,1)$, 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