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Electrons on Hexagonal Lattices and Applications to Nanotubes (2003)
Journal Article
Hartmann, B., & Zakrzewski, W. (2003). Electrons on Hexagonal Lattices and Applications to Nanotubes. Physical review B, 68(18), https://doi.org/10.1103/physrevb.68.184302

We consider a Fröhlich-type Hamiltonian on a hexagonal lattice. Aiming to describe nanotubes, we choose this two-dimensional lattice to be periodic and to have a large extension in one (x) direction and a small extension in the other (y) direction. W... Read More about Electrons on Hexagonal Lattices and Applications to Nanotubes.

CP^{N-1} Harmonic Maps and the Weierstrass Problem (2003)
Journal Article
Grundland, A., & Zakrzewski, W. (2003). CP^{N-1} Harmonic Maps and the Weierstrass Problem. Journal of Mathematical Physics, 44(8), 3370-3382. https://doi.org/10.1063/1.1586791

A Weierstrass-type system of equations corresponding to the CPN–1 harmonic maps is presented. The system constitutes a further generalization of our previous construction [J. Math. Phys. 44, 328 (2003)]. It consists of four first order equations for... Read More about CP^{N-1} Harmonic Maps and the Weierstrass Problem.

Static solutions of a D-dimensional Modified Nonlinear Schroedinger Equation (2003)
Journal Article
Brizhik, L., Eremko, A., Piette, B., & Zakrzewski, W. (2003). Static solutions of a D-dimensional Modified Nonlinear Schroedinger Equation. Nonlinearity, 16(4), 1481-1497. https://doi.org/10.1088/0951-7715/16/4/317

We study static solutions of a D-dimensional modified nonlinear Schrödinger equation (MNLSE) which was shown to describe, in two dimensions, the self-trapped (spontaneously localized) electron states in a discrete isotropic electron–phonon lattice [1... Read More about Static solutions of a D-dimensional Modified Nonlinear Schroedinger Equation.

Noncommutative planar particle dynamics with gauge interactions (2003)
Journal Article
Lukierski, J., Stichel, P., & Zakrzewski, W. (2003). Noncommutative planar particle dynamics with gauge interactions. Annals of Physics, 306(1), 78-95. https://doi.org/10.1016/s0003-4916%2803%2900010-1

We consider two ways of introducing minimal Abelian gauge interactions into the model presented in [Ann. Phys. 260 (1997) 224]. These two approaches are different only if the second central charge of the planar Galilei group is nonzero. One way leads... Read More about Noncommutative planar particle dynamics with gauge interactions.

Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories (2002)
Journal Article
Chu, C., Lukierski, J., & Zakrzewski, W. (2002). Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories. Nuclear Physics B, 632(1-3), 219-239. https://doi.org/10.1016/s0550-3213%2802%2900216-x

The IR/UV mixing and the violation of unitarity are two of the most intriguing aspects of noncommutative quantum field theories. In this paper the relation between these two phenomena is explained and established in an explicit form. We start out by... Read More about Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories.

Skyrmions from Harmonic Maps. (2001)
Book Chapter
Sutcliffe, P., & Zakrzewski, W. (2001). Skyrmions from Harmonic Maps. In H. Aratyn, & A. S. Sorin (Eds.), Integrable hierarchies and modern physical theories (215-241). Kluwer Academic Publishers. https://doi.org/10.1007/978-94-010-0720-7_7

We review some recent work on the construction of SU (N) skyrmions from rational, and more generally harmonic, maps from the two-sphere into complex projective spaces. We first describe the SU (2) case, where the rational map approximation is relativ... Read More about Skyrmions from Harmonic Maps..