The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.Comment: Revised Version. To appear in Commun. Math. Phys

We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems with short range interactions, dynamical localization implies exponential decay of ground state correlations, up to an explicit correction. Second, the dynamical localization of random xy spin chains can be reduced to dynamical localization of an effective one-particle Hamiltonian. In particular, the isotropic xy chain in random exterior magnetic field is dynamically localized.Comment: final version with minor revisions, accepted for Comm. Math. Phy

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This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a product of a deterministic unitary operator and a random unitary operator. The deterministic operator has a band structure, is absolutely continuous and plays the role of the discrete Laplacian. The random operator is diagonal with elements given by i.i.d. random phases distributed according to some absolutely continuous measure and plays the role of the random potential. In dimension one, these operators belong to the family of CMV-matrices in the theory of orthogonal polynomials on the unit circle.We implement the method of Aizenman-Molchanov to prove exponential decay of the fractional moments of the Green function for the unitary Anderson model in the following three regimes: In any dimension, throughout the spectrum at large disorder and near the band edges at arbitrary disorder and, in dimension one, throughout the spectrum at arbitrary disorder. We also prove that exponential decay of fractional moments of the Green function implies dynamical localization, which in turn implies spectral localization.These results complete the analogy with the self-adjoint case where dynamical localization is known to be true in the same three regimes.

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Background: Equine insect bite hypersensitivity (IBH) is an immediate-type hypersensitivity reaction provoked by insect-derived allergens. Icelandic horses living in Iceland do not have IBH due to absence of relevant insects, but acquire it at high frequency after being imported to mainland Europe. In contrast, their offspring born in mainland Europe has reduced IBH incidence. T helper 1 (Th1) and Th2 cells and cytokines were determined in Icelandic horses born in Iceland and on the continent and which either have IBH or are healthy. Methods: Peripheral blood mononuclear cells (PBMC) from these horses were stimulated for 18 h dur- ing summer and winter with polyclonal T cell stimuli, IBH allergen(s) or irrelevant allergen(s). Cells were analysed by flow cytometry for interferon-γ (IFN-γ) and interleukin-4 (IL-4); RNA was analysed for IFN-γ, IL-4, IL-5 and IL-13 mRNA. Results: During summer, but not during winter, IBH PBMC stimulated polyclonally showed reduced IFN-γ mRNA and IFN-γ-producing cells when compared with those of healthy horses, regardless of origin. PBMC stimulated polyclonally or with IBH allergen showed increased IL-4 mRNA levels and higher numbers of IL-4-producing cells when born in Iceland or showing IBH symptoms. IL-5 and IL-13 mRNA were modulated neither by disease nor by origin. Abrogation of IL-4 production in healthy horses born in mainland Europe may be due, at least in part, to IL-10. There was an increased level of IL-10 in supernatants from PBMC of healthy horses born in mainland Europe and stimulated polyclonally or with IBH allergen. Conclusions: Modulation of IBH incidence is governed by altered Th1/Th2 ratio, which might be influenced by IL-10.

Recurrent airway obstruction (RAO) is a common and potentially debilitating lower airway disease in horses, which shares many similarities with human asthma. In susceptible horses RAO exacerbation is caused by environmental allergens and irritants present in hay dust. The objective of this study was the identification of genes and pathways involved in the pathology of RAO by global transcriptome analyses in stimulated peripheral blood mononuclear cells (PBMCs). We performed RNA-seq on PBMCs derived from 40 RAO affected and 45 control horses belonging to three cohorts of Warmblood horses: two half-sib families and one group of unrelated horses. PBMCs were stimulated with hay dust extract, lipopolysaccharides, a recombinant parasite antigen, or left unstimulated. The total dataset consisted of 561 individual samples. We detected significant differences in the expression profiles between RAO and control horses. Differential expression (DE) was most marked upon stimulation with hay dust extract. An important novel finding was a strong upregulation of CXCL13 together with many genes involved in cell cycle regulation in stimulated samples from RAO affected horses, in addition to changes in the expression of several HIF-1 transcription factor target genes. The RAO condition alters systemic changes observed as differential expression profiles of PBMCs. Those changes also depended on the cohort and stimulation of the samples and were dominated by genes involved in immune cell trafficking, development, and cell cycle regulation. Our findings indicate an important role of CXCL13, likely macrophage or Th17 derived, and the cell cycle regulator CDC20 in the immune response in RAO.

Abstract. We introduce and analyze a class of quantum spin models defined on d-dimensional lattices Λ ⊆ Z d , which we call Product Vacua with Boundary States (PVBS). We characterize their ground state spaces on arbitrary finite volumes and study the thermodynamic limit. Using the martingale method, we prove that the models have a gapped excitation spectrum on Z d except for critical values of the parameters. For special values of the parameters we show that the excitation spectrum is gapless. We demonstrate the sensitivity of the spectrum to the existence and orientation of boundaries. This sensitivity can be explained by the presence or absence of edge excitations. In particular, we study a PVBS models on a slanted half-plane and show that it has gapless edge states but a gapped excitation spectrum in the bulk.