Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time, we find that when Nash equilibrium exists the pay off function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example where quantum game and classical game may differ. When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.Comment: 5 pages and 3 figure

Patterned growth of carbon nanotubes on Si substrates without predeposition of metal catalysts

Aligned carbon nanotubes (CNTs) can be readily synthesized on quartz or silicon-oxide-coated Si substrates using a chemical vapor deposition method, but it is difficult to grow them on pure Si substrates without predeposition of metal catalysts. We report that aligned CNTs were grown by pyrolysis of iron phthalocyanine at 1000 &deg;C on the templates created on Si substrates with simple mechanical scratching. Scanning electron microscopy and x-ray energy spectroscopy analysis revealed that the trenches and patterns created on the surface of Si substrates were preferred nucleation sites for nanotube growth due to a high surface energy, metastable surface structure, and possible capillarity effect. A two-step pyrolysis process maintained Fe as an active catalyst.<br /