Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group $G$. If $f \in L^1(G)$ has lacunary Fourier series, and vanishes on a non empty open set, then we prove that $f$ vanishes identically. This may be viewed as a qualitative uncertainty principle

Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\lambda$ is obtained for all $\lambda \in \mathfrak a^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\lambda$ away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The $L^p$-theory for the hypergeometric Fourier transform is developed for $0<p<2$. In particular, an inversion formula is proved when $1\leq p <2$

Hypergeometric functions of type BCBC and standard multiplicities

We study the Heckman-Opdam hypergeometric functions associated to a root system of type $BC$ and a multiplicity function which is allowed to assume some non-positive values (a standard multiplicity function). For such functions, we obtain positivity properties and sharp estimates which imply a characterization of the bounded hypergeometric functions. As an application, our results extend known properties of Harish-Chandra's spherical functions on Riemannian symmetric spaces of the non-compact type $G/K$ to spherical functions over homogeneous vector bundles on $G/K$ which are associated to certain small $K-$types.Comment: The present paper subsumes and extends the results of the preprint arXiv:1705.0027

Chiral Symmetry Restoration in the Schwinger Model with Domain Wall Fermions

Domain Wall Fermions utilize an extra space time dimension to provide a method for restoring the regularization induced chiral symmetry breaking in lattice vector gauge theories even at finite lattice spacing. The breaking is restored at an exponential rate as the size of the extra dimension increases. Before this method can be used in dynamical simulations of lattice QCD, the dependence of the restoration rate to the other parameters of the theory and, in particular, the lattice spacing must be investigated. In this paper such an investigation is carried out in the context of the two flavor lattice Schwinger model.Comment: LaTeX, 37 pages including 18 figures. Added comments regarding power law fitting in sect 7. Also, few changes were made to elucidate the content in sect. 5.1 and 5.3. To appear in Phys. Rev.

Stressful life events and depressive symptoms in mothers and fathers of young children

BACKGROUND: Parents of young children generally report more depressive symptoms than parents of adult children or people without children, mainly because the presence of young children increases exposure to significant stressors (such as stressful life events). However, most studies on the depressogenic role of stressful life events in parents of young children have focussed on mothers. METHODS: Using data from 1138 families with young children in Norway, we investigated gender differences in the effect of stressful life events after a child's birth on the development of parental depressive symptoms in 3 follow-ups at child's ages 3-6 years. We also explored if gender differences in disposition (personality) may explain any gender differences in the depressogenic effect of life events. RESULTS: Nesting parents within families, we found a female gender bias for both neuroticism and depressive symptoms but no gender difference in the number of life events reported. Importantly, the number of stressful life events predicted the level and course of depressive symptoms similarly for mothers and fathers. Personality traits did not change the association between stressful life events and depressive symptoms in either mothers or fathers. LIMITATIONS: Given the study design, causality cannot be inferred. CONCLUSIONS: There was no gender difference in the depressogenic effect of stressful life events in our sample. There was no evidence for a female dispositional sensitivity to the depressogenic effect of stressful life events, either. Stressful life events put both mothers and fathers of young children at risk of depression

The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice

We consider the large N limit of four dimensional SU(N) Yang-Mills field coupled to adjoint fermions on a single site lattice. We use perturbative techniques to show that the Z^4_N center-symmetries are broken with naive fermions but they are not broken with overlap fermions. We use numerical techniques to support this result. Furthermore, we present evidence for a non-zero chiral condensate for one and two Majorana flavors at one value of the lattice gauge coupling.Comment: 21 pages, 13 figures; a reference added; version to be published in JHEP, small clarifications and references adde

Influence of spin fluctuations near the Mott transition: a DMFT study

Dynamics of magnetic moments near the Mott metal-insulator transition is investigated by a combined slave-rotor and Dynamical Mean-Field Theory solution of the Hubbard model with additional fully-frustrated random Heisenberg couplings. In the paramagnetic Mott state, the spinon decomposition allows to generate a Sachdev-Ye spin liquid in place of the collection of independent local moments that typically occurs in the absence of magnetic correlations. Cooling down into the spin-liquid phase, the onset of deviations from pure Curie behavior in the spin susceptibility is found to be correlated to the temperature scale at which the Mott transition lines experience a marked bending. We also demonstrate a weakening of the effective exchange energy upon approaching the Mott boundary from the Heisenberg limit, due to quantum fluctuations associated to zero and doubly occupied sites.Comment: 6 pages, 3 figures. V3 was largely expande

Massive quenched galaxies at z~0.7 retain large molecular gas reservoirs

The physical mechanisms that quench star formation, turning blue star-forming galaxies into red quiescent galaxies, remain unclear. In this Letter, we investigate the role of gas supply in suppressing star formation by studying the molecular gas content of post-starburst galaxies. Leveraging the wide area of the SDSS, we identify a sample of massive intermediate-redshift galaxies that have just ended their primary epoch of star formation. We present ALMA CO(2-1) observations of two of these post-starburst galaxies at z~0.7 with M* ~ 2x10^11 Msun. Their molecular gas reservoirs of (6.4 +/- 0.8) x 10^9 Msun and (34.0 +/- 1.6) x 10^9 Msun are an order of magnitude larger than comparable-mass galaxies in the local universe. Our observations suggest that quenching does not require the total removal or depletion of molecular gas, as many quenching models suggest. However, further observations are required both to determine if these apparently quiescent objects host highly obscured star formation and to investigate the intrinsic variation in the molecular gas properties of post-starburst galaxies.Comment: Accepted for publication in ApJ Letters (6 pages, 5 figures

Domain wall fermion zero modes on classical topological backgrounds

The domain wall approach to lattice fermions employs an additional dimension, in which gauge fields are merely replicated, to separate the chiral components of a Dirac fermion. It is known that in the limit of infinite separation in this new dimension, domain wall fermions have exact zero modes, even for gauge fields which are not smooth. We explore the effects of finite extent in the fifth dimension on the zero modes for both smooth and non-smooth topological configurations and find that a fifth dimension of around ten sites is sufficient to clearly show zero mode effects. This small value for the extent of the fifth dimension indicates the practical utility of this technique for numerical simulations of QCD.Comment: Updated fig. 3-7, small changes in sect. 3, added fig. 8, added more reference