Hyperbolic Unit Groups and Quaternion Algebras

We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct units in a non-split quaternion algebra over R.Comment: 15 pages, this work is part of the PHd. Thesis of the third author. The paper was accepted in Proceedings Mathematical Science

Torsion-Adding and Asymptotic Winding Number for Periodic Window Sequences

In parameter space of nonlinear dynamical systems, windows of periodic states are aligned following routes of period-adding configuring periodic window sequences. In state space of driven nonlinear oscillators, we determine the torsion associated with the periodic states and identify regions of uniform torsion in the window sequences. Moreover, we find that the measured of torsion differs by a constant between successive windows in periodic window sequences. We call this phenomenon as torsion-adding. Finally, combining the torsion and the period adding rules, we deduce a general rule to obtain the asymptotic winding number in the accumulation limit of such periodic window sequences

The graphene sheet versus the 2DEG: a relativistic Fano spin-filter via STM and AFM tips

We explore theoretically the density of states (LDOS) probed by an STM tip of 2D systems hosting an adatom and a subsurface impurity,both capacitively coupled to AFM tips and traversed by antiparallel magnetic fields. Two kinds of setups are analyzed, a monolayer of graphene and a two-dimensional electron gas (2DEG). The AFM tips set the impurity levels at the Fermi energy, where two contrasting behaviors emerge: the Fano factor for the graphene diverges, while in the 2DEG it approaches zero. As result, the spin-degeneracy of the LDOS is lifted exclusively in the graphene system, in particular for the asymmetric regime of Fano interference. The aftermath of this limit is a counterintuitive phenomenon, which consists of a dominant Fano factor due to the subsurface impurity even with a stronger STM-adatom coupling. Thus we find a full polarized conductance, achievable just by displacing vertically the position of the STM tip. To the best knowledge, our work is the first to propose the Fano effect as the mechanism to filter spins in graphene. This feature arises from the massless Dirac electrons within the band structure and allows us to employ the graphene host as a relativistic Fano spin-filter

Experimental realization of the Yang-Baxter Equation via NMR interferometry

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.Comment: 10 pages and 6 figure

Characterization in bi-parameter space of a non-ideal oscillator

The authors thank scientific agencies CAPES, CNPq (112952/2015-1), and FAPESP (2011/ 19269-11). M. S. Baptista also thanks EPSRC (EP/I03 2606/1).Peer reviewedPostprin