Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions

We present a general formula for the Gaussian curvature of curved holomorphic 2-spheres in Grassmannian manifolds G(m, n). We then show how to construct such solutions with constant curvature. We also make some relevant conjectures for the admissible constant curvatures in G(m, n) and give some explicit expressions, in particular, for G(2, 4) and G(2, 5).Comment: 14 page

Heat conductivity in linear mixing systems

We present analytical and numerical results on the heat conduction in a linear mixing system. In particular we consider a quasi one dimensional channel with triangular scatterers with internal angles irrational multiples of pi and we show that the system obeys Fourier law of heat conduction. Therefore deterministic diffusion and normal heat transport which are usually associated to full hyperbolicity, actually take place in systems without exponential instability.Comment: Revtex, 4 pages, 6 EPS figure

Weak Measurement of Qubit Oscillations with Strong Response Detectors: Violation of the Fundamental Bound Imposed on Linear Detectors

We investigate the continuous weak measurement of a solid-state qubit by single electron transistors in nonlinear response regime. It is found that the signal-to-noise ratio can violate the universal upper bound imposed quantum mechanically to any linear response detectors. We understand the violation by means of the cross-correlation of the detector currents.Comment: 4 pages, 4 figure

From the social learning theory to a social learning algorithm for global optimization

Traditionally, the Evolutionary Computation (EC) paradigm is inspired by Darwinian evolution or the swarm intelligence of animals. Bandura's Social Learning Theory pointed out that the social learning behavior of humans indicates a high level of intelligence in nature. We found that such intelligence of human society can be implemented by numerical computing and be utilized in computational algorithms for solving optimization problems. In this paper, we design a novel and generic optimization approach that mimics the social learning process of humans. Emulating the observational learning and reinforcement behaviors, a virtual society deployed in the algorithm seeks the strongest behavioral patterns with the best outcome. This corresponds to searching for the best solution in solving optimization problems. Experimental studies in this paper showed the appealing search behavior of this human intelligence-inspired approach, which can reach the global optimum even in ill conditions. The effectiveness and high efficiency of the proposed algorithm has further been verified by comparing to some representative EC algorithms and variants on a set of benchmarks