We present a multi-site formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with inter-cluster hopping being treated ap
proximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multi-site formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose glass-to-superfluid transition, one an approximation based on the behaviour of the condensate fraction, and one of which relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non self-averaging is discussed.
The CLIC linear collider aims at accelerating multiple bunches of electrons and positrons and colliding them at a centre of mass energy of 3 TeV. These bunches will be accelerated through X-band linacs, operating at an accelerating frequency of 12 GH
z. Each beam readily excites wake-fields within the accelerating cavities of each linac. The transverse components of the wake-fields, if left unchecked, can dilute the beam emittance. The present CLIC design relies on heavy damping of these wake-fields in order to ameliorate the effects of the wake-fields on the beam emittance. Here we present initial results on simulations of the long-range wake-fields in these structures and on beam dynamics simulations. In particular, detailed simulations are performed, on emittance dilution due to beams initially injected with realistic offsets from the electrical centre of the cavities.
