Quantization of the Inhomogeneous Bianchi I model:quasi-Heisenberg picture

The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so called quasi-Heisenberg) equations describing explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.

The 'hard problem' and the quantum physicists. Part 1:the first generation

All four of the most important figures in the early twentieth-century development of quantum physics-Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli-had strong interests in the traditional mind-brain, or 'hard,' problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity thesis, the significance of Schroedinger's small book, 'What is life?,' the updated Platonism of Heisenberg and, perhaps most interesting of all, the interaction of Carl Jung and Wolfgang Pauli in the latter's search for a unification of mind and matter. © 2005 Elsevier Inc. All rights reserved.

Coverage versus supply cost in facility location:physics of frustrated spin systems

A comprehensive coverage is crucial for communication, supply, and transportation networks, yet it is limited by the requirement of extensive infrastructure and heavy energy consumption. Here, we draw an analogy between spins in antiferromagnet and outlets in supply networks, and apply techniques from the studies of disordered systems to elucidate the effects of balancing the coverage and supply costs on the network behavior. A readily applicable, coverage optimization algorithm is derived. Simulation results show that magnetized and antiferromagnetic domains emerge and coexist to balance the need for coverage and energy saving. The scaling of parameters with system size agrees with the continuum approximation in two dimensions and the tree approximation in random graphs. Due to frustration caused by the competition between coverage and supply cost, a transition between easy and hard computation regimes is observed. We further suggest a local expansion approach to greatly simplify the message updates which shed light on simplifications in other problems. © 2014 American Physical Society.