Ferromagnetic ground states of the Hubbard model on a complete graph

We use group theory to derive the exact analytical expression of the ferromagnetic ground states of the Hubbard model on a complete graph for arbitrary lattice sites f and for arbitrary fillings $N$. We find that for $t>0$ and for $N=f+1$ the ground state is maximally ferromagnetic with total spin $S=(f-1)/2$. For $N > f+1$ the ground state is still ferromagnetic but becomes degenerate with respect to $S$.Comment: latex fil

Matter wave quantum dots (anti-dots) in ultracold atomic Bose-Fermi mixtures

The properties of ultracold atomic Bose-Fermi mixtures in external potentials are investigated and the existence of gap solitons of Bose-Fermi mixtures in optical lattices demonstrated. Using a self-consistent approach we compute the energy spectrum and show that gap solitons can be viewed as matter wave realizations of quantum dots (anti-dots) with the bosonic density playing the role of trapping (expulsive) potential for the fermions. The fermionic states trapped in the condensate are shown to be at the bottom of the Fermi sea and therefore well protected from thermal decoherence. Energy levels, filling factors and parameters dependence of gap soliton quantum dots are also calculated both numerically and analytically.Comment: Extended version of talk given at the SOLIBEC conference, Almagro, Spain, 8-12 February 2005. To be published on Phys.Rev.

Stabilization of ratchet dynamics by weak periodic signals

We study the influence of weak periodic signals on the transport properties of underdamped ratchets. We find that the constant current intervals related to the ratchet, can be significantly enlarged by a weak subharmonic signal which is in phase with the internal driver. This stabilization phenomenon is found to exist both in absence and in presence of noise. The dependence of this effect on the phase of the applied signal is also investigated.Comment: tex + 4 figures.ps in a .tar archive / submitted to PR

Logarithmic divergence of the block entanglement entropy for the ferromagnetic Heisenberg model

Recent studies have shown that logarithmic divergence of entanglement entropy as function of size of a subsystem is a signature of criticality in quantum models. We demonstrate that the ground state entanglement entropy of $n$ sites for ferromagnetic Heisenberg spin-1/2 chain of the length $L$ in a sector with fixed magnetization $y$ per site grows as ${1/2}\log_{2} \frac{n(L-n)}{L}C(y)$, where $C(y)=2\pi e({1/4}-y^{2})$Comment: 4 pages, 2 fig

Gap-Townes solitons and localized excitations in low dimensional Bose Einstein condensates in optical lattices

We discuss localized ground states of Bose-Einstein condensates in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schr\"odinger equation which extends the Gross-Pitaevskii equation to the one dimensional case. We use both a variational method and a self-consistent approach to show the existence of unstable localized excitations which are similar to Townes solitons of the cubic nonlinear Schr\"odinger equation in two dimensions. These solutions are shown to be located in the forbidden zones of the band structure, very close to the band edges, separating decaying states from stable localized ones (gap-solitons) fully characterizing their delocalizing transition. In this context usual gap solitons appear as a mechanism for arresting collapse in low dimensional BEC in optical lattices with attractive real three-body interaction. The influence of the imaginary part of the three-body interaction, leading to dissipative effects on gap solitons and the effect of atoms feeding from the thermal cloud are also discussed. These results may be of interest for both BEC in atomic chip and Tonks-Girardeau gas in optical lattices