Hasil untuk "math-ph"

G. Duncan, Chantelle J. Dowsett, A. Claessens et al.

Allan Wigfield, J. Meece

Yuezhao Li

We study the robustness of topological phases on aperiodic lattices by constructing *-homomorphisms from the groupoid model to the coarse-geometric model of observable C*-algebras. These *-homomorphisms induce maps in K-theory and Kasparov theory. We show that the strong topological phases in the groupoid model are detected by position spectral triples. We show that topological phases coming from stacking along another Delone set are always weak in the coarse-geometric sense.

Oliver Siebert

We study the dynamics of non-relativistic fermions in $\mathbb R^d$ interacting through a pair potential. Employing methods developed by Buchholz in the framework of resolvent algebras, we identify an extension of the CAR algebra where the dynamics acts as a group of *-automorphisms, which are continuous in time in all sectors for fixed particle numbers. In addition, we identify a suitable dense subalgebra where the time evolution is also strongly continuous. Finally, we briefly discuss how this framework could be used to construct KMS states in the future.

Brian A. Nosek, M. Banaji, A. Greenwald

D. Hopko, R. Mahadevan, Robert L. Bare et al.

A. Schoenfeld

Bin Gui

For a vertex operator algebra $V$, we construct an explicit isomorphism between the space of genus-0 conformal blocks associated to permutation-twisted $V^{\otimes n}$-modules and the space of conformal blocks associated to untwisted $V$-modules and a branched covering C of the Riemann sphere. As a consequence, when V is CFT-type, rational, and C2 cofinite, the fusion rules for permutation-twisted modules are determined. We also relate the sewing and factorization of permutation-twisted $V^{\otimes n}$-conformal blocks and untwisted $V$-conformal blocks. Various applications are discussed. Note the differences in theorem and equation numbering between the arXiv version and the published version. Some terminology also varies: See Def. 2.2.1 (Def. 2.20 of the published version) for a slight difference in the meanings of $\mathbb U$. The term "Analytic Jacobi identity" in the arXiv version is called the "duality property" in the published version.

Kimberly Hufferd-Ackles, K. Fuson, M. Sherin

T. Schmader, Michael Johns, Marchelle Barquissau

Tadahiro Oh, Kihoon Seong, Leonardo Tolomeo

We study Gibbs measures with log-correlated base Gaussian fields on the $d$-dimensional torus. In the defocusing case, the construction of such Gibbs measures follows from Nelson's argument. In this paper, we consider the focusing case with a quartic interaction. Using the variational formulation, we prove non-normalizability of the Gibbs measure. When $d = 2$, our argument provides an alternative proof of the non-normalizability result for the focusing $Φ^4_2$-measure by Brydges and Slade (1996). Furthermore, we provide a precise rate of divergence, where the constant is characterized by the optimal constant for a certain Bernstein's inequality on $\mathbb{R}^d$. We also go over the construction of the focusing Gibbs measure with a cubic interaction. In the appendices, we present (a) non-normalizability of the Gibbs measure for the two-dimensional Zakharov system and (b) the construction of focusing quartic Gibbs measures with smoother base Gaussian measures, showing a critical nature of the log-correlated Gibbs measure with a focusing quartic interaction.

C. Good, Joshua Aronson, Jayne Ann Harder

M. Steffens, Petra Jelenec, P. Noack

Elia Bisi, Nikos Zygouras

We study the combinatorial structure of the irreducible characters of the classical groups ${\rm GL}_n(\mathbb{C})$, ${\rm SO}_{2n+1}(\mathbb{C})$, ${\rm Sp}_{2n}(\mathbb{C})$, ${\rm SO}_{2n}(\mathbb{C})$ and the "non-classical" odd symplectic group ${\rm Sp}_{2n+1}(\mathbb{C})$, finding new connections to the probabilistic model of Last Passage Percolation (LPP). Perturbing the expressions of these characters as generating functions of Gelfand-Tsetlin patterns, we produce two families of symmetric polynomials that interpolate between characters of ${\rm Sp}_{2n}(\mathbb{C})$ and ${\rm SO}_{2n+1}(\mathbb{C})$ and between characters of ${\rm SO}_{2n}(\mathbb{C})$ and ${\rm SO}_{2n+1}(\mathbb{C})$. We identify the first family as a one-parameter specialization of Koornwinder polynomials, for which we thus provide a novel combinatorial structure; on the other hand, the second family appears to be new. We next develop a method of Gelfand-Tsetlin pattern decomposition to establish identities between all these polynomials that, in the case of irreducible characters, can be viewed as branching rules. Through these formulas we connect orthogonal and symplectic characters, and more generally the interpolating polynomials, to LPP models with various symmetries, thus going beyond the link with classical Schur polynomials originally found by Baik and Rains (Duke Math. J., 2001). Taking the scaling limit of the LPP models, we finally provide an explanation of why the Tracy-Widom GOE and GSE distributions from random matrix theory admit formulations in terms of both Fredholm determinants and Fredholm Pfaffians.

Brian A. Nosek, Frederick L. Smyth

Gender stereotypes about math and science do not need to be endorsed, or even available to conscious introspection, to contribute to the sex gap in engagement and achievement in science, technology, engineering, and mathematics (STEM). The authors examined implicit math attitudes and stereotypes among a heterogeneous sample of 5,139 participants. Women showed stronger implicit negativity toward math than men did and equally strong implicit gender stereotypes. For women, stronger implicit math=male stereotypes predicted greater negativity toward math, less participation, weaker self-ascribed ability, and worse math achievement; for men, those relations were weakly in the opposite direction. Implicit stereotypes had greater predictive validity than explicit stereotypes. Female STEM majors, especially those with a graduate degree, held weaker implicit math=male stereotypes and more positive implicit math attitudes than other women. Implicit measures will be a valuable tool for education research and help account for unexplained variation in the STEM sex gap.

G. Stahl

T. Cleary, Peggy P. Chen

Carlo Tomasetto, F. Alparone, M. Cadinu

P. H. Fisher

P. Jensen, A. Rasmussen