Superfluid/ferromagnet/superfluid junction and π\pi-phase in a superfluid Fermi gas

We investigate the possibility of superfluid/ferromagnet/superfluid (SFS)-junction in a superfluid Fermi gas. To examine this possibility in a simple manner, we consider an attractive Hubbard model at $T=0$ within the mean-field theory. When a potential barrier is embedded in a superfluid Fermi gas with population imbalance ($N_\uparrow>N_\downarrow$, where $N_\sigma$ is the number of atoms with pseudospin $\sigma=\uparrow,\downarrow$), this barrier is shown to be {\it magnetized} in the sense that excess $\uparrow$-spin atoms are localized around it. The resulting superfluid Fermi gas is spatially divided into two by this {\it ferromagnet}, so that one obtains a junction similar to the superconductor/ferromagnet/superconductor-junction discussed in superconductivity. Indeed, we show that the so-called $\pi$-phase, which is a typical phenomenon in the SFS-junction, is realized, where the superfluid order parameter changes its sign across the junction. Our results would be useful for the study of magnetic effects on fermion superfluidity using an ultracold Fermi gas.Comment: 22 pages, 14 figure

Standard imsets for undirected and chain graphical models

We derive standard imsets for undirected graphical models and chain graphical models. Standard imsets for undirected graphical models are described in terms of minimal triangulations for maximal prime subgraphs of the undirected graphs. For describing standard imsets for chain graphical models, we first define a triangulation of a chain graph. We then use the triangulation to generalize our results for the undirected graphs to chain graphs.Comment: Published at http://dx.doi.org/10.3150/14-BEJ611 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm