23,592 research outputs found
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
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
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