For the eigenvalues of p complex Hermitian n × n matrices coupled in a chain, we give a method of calculating the spacing functions. This is a generalization of the one-matrix case which has been known for a long time. †

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In this paper, we study charged spin-1/2 particles in two dimensions, subjected to a perpendicular non-Abelian magnetic field. Specializing to a choice of vector potential that is spatially constant but non-Abelian, we investigate the Landau level spectrum in planar and spherical geometry, paying particular attention to the role of the total angular momentum J = L + S. Then, we show that the adiabatic insertion of non-Abelian flux in a spin-polarized quantum Hall state leads to the formation of charged spin textures, which in the simplest cases can be identified with quantum Hall Skyrmions.

The functional consequences of local and global dynamics can be very different in natural systems. Many such systems have a network description that exhibits strong local clustering as well as high communication efficiency, often termed as small-world networks (SWN). We show that modular organization in otherwise random networks generically give rise to SWN, with a characteristic time-scale separation between fast intra-modular and slow inter-modular processes. The universality of this dynamical signature, that distinguishes modular networks from earlier models of SWN, is demonstrated by processes as different as spin-ordering, synchronization and diffusion.