Band-Structure Effects in the Spin Relaxation of Conduction Electrons

Spin relaxation of conduction electrons in metals is significantly influenced by the Fermi surface topology. Electrons near Brillouin zone boundaries, special symmetry points, or accidental degeneracy lines have spin flip rates much higher than an average electron. A realistic calculation and analytical estimates show that these regions dominate the spin relaxation, explaining why polyvalent metals have much higher spin relaxation rates (up to three orders of magnitude) than similar monovalent metals. This suggests that spin relaxation in metals can be tailored by band-structure modifications like doping, alloying, reducing the dimensionality, etc.Comment: 10 pages, 2 figures; to appear in the 43rd MMM Conference Proceedings published in the JA

Robust Computer Algebra, Theorem Proving, and Oracle AI

In the context of superintelligent AI systems, the term "oracle" has two meanings. One refers to modular systems queried for domain-specific tasks. Another usage, referring to a class of systems which may be useful for addressing the value alignment and AI control problems, is a superintelligent AI system that only answers questions. The aim of this manuscript is to survey contemporary research problems related to oracles which align with long-term research goals of AI safety. We examine existing question answering systems and argue that their high degree of architectural heterogeneity makes them poor candidates for rigorous analysis as oracles. On the other hand, we identify computer algebra systems (CASs) as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem provers, systems which have largely been developed independent of one another, provide a concrete set of problems related to the notion of provable safety that has emerged in the AI safety community. We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical software projects for scientists interested in AI safety.Comment: 15 pages, 3 figure