We prove the existence of a set of two-scale magnetic Wannier orbitals, wmn(r), in the infinite plane. The quantum numbers of these states are the positions (m,n) of their centers which form a von Neumann lattice. Function w00(r) localized at the origin has a nearly Gaussian shape of exp(−r2/4l2)/ √ 2π for r ∼ √ 2πl, where l is the magnetic length. This region makes a dominating contribution to...

We demonstrate that the fusion algebra of conformal defects of a two-dimensional conformal field theory contains information about the internal symmetries of the theory and allows one to read off generalizations of Kramers-Wannier duality. We illustrate the general mechanism in the examples of the Ising model and the three-state Potts model.

We investigate from first principles the proposed destruction of the controversial e(')g pockets in the Fermi surface of Na(x)CoO(2) due to Na disorder, by calculating its k-dependent configuration-averaged spectral function . To this end, a Wannier function-based method is developed that treats the effects of disorder beyond the mean field. Remarkable spectral broadenings of order ∼1  ...

The electron-impact ionization cross section for hydrogen near threshold is calculated using both timedependent wave-packet and time-dependent Green’s-function methods. The time-dependent Green’s-function method also allows the calculation of the elastic cross section. The need for absorbing potentials was removed by allowing our fast waves to leave our two-dimensional grid. Two different model...

We consider the classical duality result of Kramers and Wannier, which expresses the partition function of the twodimensional Ising model at low temperature in terms of the partition function of the two-dimensional Ising model at high temperature. Our main contribution is to gain new insights into this result by reproving it with the help of a simple normalfactor-graph duality theorem (with ori...

Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...