Amplitude Relations in Non-linear Sigma Model

In this paper, we investigate tree-level scattering amplitude relations in $U(N)$ non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [23,24] both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization. We prove the off-shell $U(1)$ identity and fundamental BCJ relation for even-point currents. By taking the on-shell limits of the off-shell relations, we show that the color-ordered tree amplitudes with even points satisfy $U(1)$-decoupling identity and fundamental BCJ relation, which have the same formations within Yang-Mills theory. We further state that all the on-shell general KK, BCJ relations as well as the minimal-basis expansion are also satisfied by color-ordered tree amplitudes. As a consequence of the relations among color-ordered amplitudes, the total $2m$-point tree amplitudes satisfy DDM form of color decomposition as well as KLT relation.Comment: 27 pages, 8 figures, 4 tables, JHEP style, improved versio

Continuous-Variable Quantum Games

We investigate the quantization of games in which the players can access to a continuous set of classical strategies, making use of continuous-variable quantum systems. For the particular case of the Cournot's Duopoly, we find that, even though the two players both act as "selfishly" in the quantum game as they do in the classical game, they are found to virtually cooperate due to the quantum entanglement between them. We also find that the original Einstein-Podolksy-Rosen state contributes to the best profits that the two firms could ever attain. Moreover, we propose a practical experimental setup for the implementation of such quantum games.Comment: 3 figure

Adaptive minimum symbol error rate beamforming assisted receiver for quadrature amplitude modulation systems

An adaptive beamforming assisted receiver is proposed for multiple antenna aided multiuser systems that employ bandwidth efficient quadrature amplitude modulation (QAM). A novel minimum symbol error rate (MSER) design is proposed for the beamforming assisted receiver, where the system’s symbol error rate is directly optimized. Hence the MSER approach provides a significant symbol error ratio performance enhancement over the classic minimum mean square error design. A sample-by-sample adaptive algorithm, referred to as the least symbol error rate (LBER) technique, is derived for allowing the adaptive implementation of the system to arrive from its initial beamforming weight solution to MSER beamforming solution