On the formation of active region prominences (H alpha filaments)

Analysis of sequential H alpha images of active region prominence formation suggests that simple large-scale photospheric mass-motions may play a key role in the formation of these long, thin, H alpha filaments

Unimodular graphs and Eisenstein sums

Motivated in part by combinatorial applications to certain sum-product phenomena, we introduce unimodular graphs over finite fields and, more generally, over finite valuation rings. We compute the spectrum of the unimodular graphs, by using Eisenstein sums associated to unramified extensions of such rings. We derive an estimate for the number of solutions to the restricted dot product equation $a\cdot b=r$ over a finite valuation ring. Furthermore, our spectral analysis leads to the exact value of the isoperimetric constant for half of the unimodular graphs. We also compute the spectrum of Platonic graphs over finite valuation rings, and products of such rings - e.g., $\mathbb{Z}/(N)$. In particular, we deduce an improved lower bound for the isoperimetric constant of the Platonic graph over $\mathbb{Z}/(N)$.Comment: V2: minor revisions. To appear in the Journal of Algebraic Combinatoric

Spectral morphisms, K-theory, and stable ranks

We give a brief account of the interplay between spectral morphisms, K-theory, and stable ranks in the context of Banach algebras.Comment: 12 pages; to appear in the Proceedings of the Workshop on Noncommutative Geometry (Fields Institute, Toronto 2008

Fidelity approach to quantum phase transitions in quantum Ising model

Fidelity approach to quantum phase transitions uses the overlap between ground states of the system to gain some information about its quantum phases. Such an overlap is called fidelity. We illustrate how this approach works in the one dimensional quantum Ising model in the transverse field. Several closed-form analytical expressions for fidelity are discussed. An example of what insights fidelity provides into the dynamics of quantum phase transitions is carefully described. The role of fidelity in central spin systems is pointed out.Comment: Proceedings of the 50th Karpacz Winter School of Theoretical Physics, Karpacz, Poland, 2-9 March 201