Quantum phase transition in an atomic Bose gas near a Feshbach resonance

We study the quantum phase transition in an atomic Bose gas near a Feshbach resonance in terms of the renormalization group. This quantum phase transition is characterized by an Ising order parameter. We show that in the low temperature regime where the quantum fluctuations dominate the low-energy physics this phase transition is of first order because of the coupling between the Ising order parameter and the Goldstone mode existing in the bosonic superfluid. However, when the thermal fluctuations become important, the phase transition turns into the second order one, which belongs to the three-dimensional Ising universality class. We also calculate the damping rate of the collective mode in the phase with only a molecular Bose-Einstein condensate near the second-order transition line, which can serve as an experimental signature of the second-order transition.Comment: 8 pages, 2 figures, published version in Phys. Rev.

New critical behavior in unconventional ferromagnetic superconductors

New critical behavior in unconventional superconductors and superfluids is established and described by the Wilson-Fisher renormalization-group method. For certain ordering symmetries a new type of fluctuation-driven first order phase transitions at finite and zero temperature are predicted. The results can be applied to a wide class of ferromagnetic superconducting and superfluid systems, in particular, to itinerant ferromagnets as UGe2 and URhGe.Comment: 12 pages, 6 fig

Gaussian limits for generalized spacings

Nearest neighbor cells in $R^d,d\in\mathbb{N}$, are used to define coefficients of divergence ($\phi$-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a variance depending on the underlying point density. In $d=1$, this extends classical central limit theory for sum functions of spacings. The general results yield central limit theorems for logarithmic $k$-spacings, information gain, log-likelihood ratios and the number of pairs of sample points within a fixed distance of each other.Comment: Published in at http://dx.doi.org/10.1214/08-AAP537 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org