The low-dimensional structures formed by tricategories

We form tricategories and the homomorphisms between them into a bicategory, whose 2-cells are certain degenerate tritransformations. We then enrich this bicategory into an example of a three-dimensional structure called a locally cubical bicategory, this being a bicategory enriched in the monoidal 2-category of pseudo double categories. Finally, we show that every sufficiently well-behaved locally cubical bicategory gives rise to a tricategory, and thereby deduce the existence of a tricategory of tricategories.Comment: 41 pages; v2: final journal versio

Pure spin photocurrents in low-dimensional structures

As is well known the absorption of circularly polarized light in semiconductors results in optical orientation of electron spins and helicity-dependent electric photocurrent, and the absorption of linearly polarized light is accompanied by optical alignment of electron momenta. Here we show that the absorption of unpolarized light leads to generation of a pure spin current, although both the average electron spin and electric current vanish. We demonstrate this for direct interband and intersubband as well as indirect intraband (Drude-like) optical transitions in semiconductor quantum wells (QWs).Comment: 4 pages, 3 figure

Two interacting diffusing particles on low-dimensional discrete structures

In this paper we study the motion of two particles diffusing on low-dimensional discrete structures in presence of a hard-core repulsive interaction. We show that the problem can be mapped in two decoupled problems of single particles diffusing on different graphs by a transformation we call 'diffusion graph transform'. This technique is applied to study two specific cases: the narrow comb and the ladder lattice. We focus on the determination of the long time probabilities for the contact between particles and their reciprocal crossing. We also obtain the mean square dispersion of the particles in the case of the narrow comb lattice. The case of a sticking potential and of 'vicious' particles are discussed.Comment: 9 pages, 6 postscript figures, to appear in 'Journal of Physics A',-January 200

Structure of the Fulde-Ferrell-Larkin-Ovchinnikov state in two-dimensional superconductors

Nonuniform superconducting state due to strong spin magnetism is studied in two-dimensional type-II superconductors near the second order phase transition line between the normal and the superconducting states. The optimum spatial structure of the orderparameter is examined in systems with cylindrical symmetric Fermi surfaces. It is found that states with two-dimensional structures have lower free energies than the traditional one-dimensional solutions, at low temperatures and high magnetic fields. For s-wave pairing, triangular, square, hexagonal states are favored depending on the temperature, while square states are favored at low temperatures for d-wave pairing. In these states, orderparameters have two-dimensional structures such as square and triangular lattices.Comment: 11 pages (LaTeX, revtex.sty), 3 figures; added reference

Very low sensitivity FIR filter implementation using 'structural passivity' concept

The concept of "structurally bounded" or "structurally passive" FIR filter implementation is introduced, as a means of achieving very low passband sensitivities. The resulting filter structures, called FIRBR structures, can easily be transformed into very low-sensitivity "passive" two-dimensional FIR filter structures. From a layout point of view, the new structures are not any more complicated than the well-known cascade form. The FIRBR structures do not depend, for synthesis, upon continuous-time filter circuits