We report on transport properties of the super-honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight-binding approximation. This super-honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. The super-honeycomb lattice also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat-band mode of the super-honeycomb will be excited and the input beams will exhibit strong localization during propagation. On the other hand, if the modes of Dirac cones of the super-honeycomb lattice are excited, one will observe conical diffraction. Furthermore, if the input beam is properly chosen to excite a sublattice of the super-honeycomb lattice and the modes of Dirac cones with different pseudospins, e.g., the three-beam interference pattern, the pseudospin-mediated vortices will be observed.

The effect of spin-involved interaction on the transport properties of disordered two-dimensional electron systems with ferromagnetic contacts is described using a two-component model. Components representing spin-up and spin-down states are supposed to be coupled at a discrete set of points. We have found that due to the additional interference arising in two-component systems the difference between conductances for the parallel and antiparallel orientations of the contact magnetization changes its sign as a function of the length of the conducting channel.

We investigate non-equilibrium particle transport in a system consisting of a geometric scatterer and two leads coupled to heat baths with different chemical potentials. We derive an expression for the corresponding current, the carriers of which are fermions, and analyze numerically its dependence on the model parameters in examples where the scatterer has a rectangular or triangular shape.

In this paper, we present and prove the first closed formula bounding the degree of regularity of an HFE system over an arbitrary finite field. Though these bounds are not necessarily optimal, they can be used to deduce 1. if D, the degree of the corresponding HFE polynomial, and q, the size of the corresponding finite field, are fixed, inverting HFE system is polynomial for all fields; 2. if D is of the scale O(n^α) where n is the number of variables in an HFE system, and q is fixed, inverting HFE systems is quasi-polynomial for all fields. We generalize and prove rigorously similar results by Granboulan, Joux and Stern in the case when q = 2 that were communicated at Crypto 2006.

We investigate approximations of the vertex coupling on a star-shaped graph by families of operators with singularly scaled rank-one interactions. We find a family of vertex couplings, generalizing the <i></i>-interaction on the line, and show that with a suitable choice of the parameters they can be approximated in this way in the norm-resolvent sense. We also analyze spectral properties of the involved operators and demonstrate the convergence of the corresponding on-shell scattering matrices.