Roland Münzner

Antiferromagnetic phase in the Hubbard model by means of the composite operator method

We have investigated the antiferromagnetic phase of two-dimensional (2D), three-dimensional (3D), and extended Hubbard models on a bipartite cubic lattice by means of the composite operator method within a two-pole approximation. This approach yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of both the model and the algebra. The complete phase diagram, as regards the antiferromagnetic and paramagnetic phases, has been drawn. We first reported, within a pole approximation, three kinds of transitions at half-filling: Mott-Hubbard, Mott-Heisenberg, and Heisenberg transitions. We have also found a metal-insulator transition, driven by doping, within the antiferromagnetic phase. This latter is restricted to a very small region near half-filling, and has, in contrast to what has been found by similar approaches, a finite critical Coulomb interaction as a lower bound at half-filling. Finally, it is worth noting that our antiferromagnetic gap has two independent components: one due to the antiferromagnetic correlations, and another coming from the Mott-Hubbard mechanism.

Calculation of imaging errors of AWG

This paper reports on the modeling of arrayed-waveguide gratings (AWGs) by means of Fourier optics where the coupling between the grating waveguides and defocus of the star couplers is taken into account as well. Special interest is drawn to the geometrical modeling of AWGs. The paraxial approximation for the free-space propagation within the star couplers, the exact calculation of the coupling coefficients for the star couplers by an orthonormal basis (ONB) expansion, and the drawbacks due to the nonunitary transfer matrix provided by the Greens functions approach for the coupling between the grating waveguides, as well as possible improvements thereof, are identified as crucial points. An efficient orthonormalization procedure by means of an eigenvector decomposition is presented. A unitary approximation of the transfer matrix, which is in itself approximate but in general not unitary, introduced within the impulse response method, is obtained. The presented simulation technique allows for ab initio simulations, which do not fall back on any experimental input, for the spectral response of AWGs, which are found in good agreement with experimental results.

Imaging errors in arrayed waveguide gratings

A detailed assessment of imaging errors in arrayed waveguide gratings (AWG) is presented, focussing on possible design related imaging errors as well as on typical imaging errors mediated by the fabrication process. From a design point of view, special interest is drawn to the effect of coupling within the array of grating waveguides and to the impact of the paraxial approximation for the star couplers which is commonly used in the design of AWGs. Both become important design issues affecting the performance of AWG devices when moving to high numbers of narrowly spaced channels. For the technology related imaging errors we focus on one side on the impact of almost uncorrelated phase errors at high spatial frequencies. They can typically be attributed to fluctuations in the index profile and waveguide dimensions in the grating region. On the other side correlated long range phase errors are treated which occur in the grating region as well as within the star couplers and which are typical for stress induced index changes in silica-on-silicon waveguides. It is shown that only modelling tools which include all types of the above imaging effects can provide reliable boundary conditions for a comprehensive design of high end AWG concerning spectral shape and chromatic dispersion.

Antiferromagnetism in the 2D Hubbard model: phase transition and local quantities

Abstract We present a first study of the antiferromagnetic state in the 2D U–t–t′ model at finite temperatures by the composite operator method, providing simultaneously a fully self-consistent treatment of the paramagnetic and the AF phase. Near half-filling the critical value of the Coulomb repulsion as a function of t′ and the temperature dependence of the magnetization and of the internal energy per site have been studied.

Ferromagnetic order for the 2D extended Hubbard model

Abstract The 2D extended Hubbard model is studied by means of the composite operator method, in presence of ferromagnetic order. A fully self-consistent procedure, based on the use of the Pauli principle symmetry constraint, permits the evaluation of the magnetic phase diagram of the model.

Global C*-Dynamics and Its KMS States of Weakly Inhomogeneous Bipolaronic Superconductors

We establish the limiting dynamics of a class of inhomogeneous bipolaronic models for superconductivity which incorporate deviations from the homogeneous models strong enough to require disjoint representations. The models are of the Hubbard type and the thermodynamics of their homogeneous part has been already elaborated by the authors. Now the dynamics of the systems is evaluated in terms of a generalized perturbation theory and leads to a C*-dynamical system over a classically extended algebra of observables. The classical part of the dynamical system, expressed by a set of 15 nonlinear differential equations, is observed to be independent from the perturbations. The KMS states of the C*-dynamical system are determined on the state space of the extended algebra of observables. The subsimplices of KMS states with unbroken symmetries are investigated and used to define the “type” of a phase. The KMS phase diagrams are worked out explicitly and compared with the thermodynamic phase structures obtained in the preceding works.

Exact ab-initio modeling of arrayed-waveguide gratings

For the first time a complete ab-initio calculation of AWGs including coupling and defocus is presented. The full paraxial approximation together with an ortho-normal basis (ONB) expansion of the modes and a unitary approximation of the transfer matrix is used.