Stability of Ferromagnetism in Hubbard models with degenerate single-particle ground states

A Hubbard model with a N_d-fold degenerate single-particle ground state has ferromagnetic ground states if the number of electrons is less or equal to N_d. It is shown rigorously that the local stability of ferromagnetism in such a model implies global stability: The model has only ferromagnetic ground states, if there are no single spin-flip ground states. If the number of electrons is equal to N_d, it is well known that the ferromagnetic ground state is unique if and only if the single-particle density matrix is irreducible. We present a simplified proof for this result.Comment: accepted for publication in J. Phys.

Bose-Hubbard model on two-dimensional line graphs

We construct a basis for the many-particle ground states of the positive hopping Bose-Hubbard model on line graphs of finite 2-connected planar bipartite graphs at sufficiently low filling factors. The particles in these states are localized on non-intersecting vertex-disjoint cycles of the line graph which correspond to non-intersecting edge-disjoint cycles of the original graph. The construction works up to a critical filling factor at which the cycles are close-packed.Comment: 9 pages, 5 figures, figures and conclusions update

Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands

We introduce and study two classes of Hubbard models with magnetic flux or with spin-orbit coupling, which have a flat lowest band separated from other bands by a nonzero gap. We study the Chern number of the flat bands, and find that it is zero for the first class but can be nontrivial in the second. We also prove that the introduction of on-site Coulomb repulsion leads to ferromagnetism in both the classes.Comment: 6 pages, 5 figure

Stability of patterns with arbitrary period for a Ginzburg-Landau equation with a mean field

We consider the following system of equations A_t= A_{xx} + A - A^3 -AB,\quad x\in R,\,t>0, B_t = \sigma B_{xx} + \mu (A^2)_{xx}, x\in R, t>0, where \mu > \sigma >0. It plays an important role as a Ginzburg-Landau equation with a mean field in several fields of the applied sciences. We study the existence and stability of periodic patterns with an arbitrary minimal period L. Our approach is by combining methods of nonlinear functional analysis such as nonlocal eigenvalue problems and the variational characterization of eigenvalues with Jacobi elliptic integrals. This enables us to give a complete characterization of existence and stability for all solutions with A>0, spatial average =0 and an arbitrary minimal period

Medications for chronic pain a practical review

A journal article on medication for chronic pain in HIV/AIDS patients in Sub-Saharan Africa.This review is confined to the drug management of chronic pain, and is specifically adapted to the resource- poor environment and the HIV pandemic of sub-Saharan Africa. A brief classification of chronic pain is followed by a discussion of the different classes of medications in use, including those used in migraine. An approach to the rational drug management of neuropathic pain is presented. In conclusion some general principles for prescribing in this setting are derived

Flat-band excitonic states in Kagome lattice on semiconductor surface

Excitonic properties in the Kagome lattice system, which is produced by quantum wires on semiconductor surfaces, are investigated by using the exact diagonalization of a tight binding model. It is shown that due to the existence of flat bands the binding energy of exciton becomes remarkably large in the two-dimensional Kagome lattice compared to that in one-dimensional lattice, and the exciton Bohr radius is quite small as large as a lattice constant. We also discuss the magnetic field effects on the exciton binding energy and the stability of exciton against the creation of charged exciton and biexciton.Comment: 5 pages, 5 figure

Design of multivariable feedback control systems via spectral assignment

The applicability of spectral assignment techniques to the design of multivariable feedback control systems was investigated. A fractional representation design procedure for unstable plants is presented and illustrated with an example. A computer aided design software package implementing eigenvalue/eigenvector design procedures is described. A design example which illustrates the use of the program is explained

Relationship between spiral and ferromagnetic states in the Hubbard model in the thermodynamic limit

We explore how the spiral spin(SP) state, a spin singlet known to accompany fully-polarized ferromagnetic (F) states in the Hubbard model, is related with the F state in the thermodynamic limit using the density matrix renormalization group and exact diagonalization. We first obtain an indication that when the F state is the ground state the SP state is also eligible as the ground state in that limit. We then follow the general argument by Koma and Tasaki [J. Stat. Phys. {\bf 76}, 745 (1994)] to find that: (i) The SP state possesses a kind of order parameter. (ii) Although the SP state does not break the SU(2) symmetry in finite systems, it does so in the thermodynamic limit by making a linear combination with other states that are degenerate in that limit. We also calculate the one-particle spectral function and dynamical spin and charge susceptibilities for various 1D finite-size lattices. We find that the excitation spectrum of the SP state and the F state is almost identical. Our present results suggest that the SP and the F states are equivalent in the thermodynamic limit. These properties may be exploited to determine the magnetic phase diagram from finite-size studies.Comment: 17 figures, to be published in Phys. Rev.