Norm convergence of nilpotent ergodic averages

We show that multiple polynomial ergodic averages arising from nilpotent groups of measure preserving transformations of a probability space always converge in the L^2 norm.Comment: 17 pages. Added further results and example

The inverse sieve problem in high dimensions

We show that if a big set of integer points in [0,N]^d, d>1, occupies few residue classes mod p for many primes p, then it must essentially lie in the solution set of some polynomial equation of low degree. This answers a question of Helfgott and Venkatesh.Comment: 15 pages. Added more examples in Section 5 and some minor change

The Cabibbo-Kobayashi-Maskawa density matrices

The flavor changing charged currents of the weak sector of the Standard Model are studied in the framework of a quantum statistical approach. The quantum superposition of same-type quarks, generated by the Cabibbo-Kobayashi-Maskawa matrix, is used to define three density matrices, one for each quark family. The properties of such density matrices are analyzed, in particular, the associated von Neumann entropy. It is proven that, due to the unitarity of the Cabibbo-Kobayashi-Maskawa matrix, the quantum mixtures of quarks resulting from the weak interaction do not increase entropy and, therefore, the violation of CP and T symmetries cannot be related to the second law of thermodynamics.Comment: 3 page

Tricritical Point in Quantum Phase Transitions of the Coleman-Weinberg Model at Higgs Mass

The tricritical point, which separates first and second order phase transitions in three-dimensional superconductors, is studied in the four-dimensional Coleman-Weinberg model, and the similarities as well as the differences with respect to the three-dimensional result are exhibited. The position of the tricritical point in the Coleman-Weinberg model is derived and found to be in agreement with the Thomas-Fermi approximation in the three-dimensional Ginzburg-Landau theory. From this we deduce a special role of the tricritical point for the Standard Model Higgs sector in the scope of the latest experimental results, which suggests the unexpected relevance of tricritical behavior in the electroweak interactions.Comment: 5 pages, 1 figure, published in Phys. Lett.

Benchmark calculations for reduced density-matrix functional theory

Reduced density-matrix functional theory (RDMFT) is a promising alternative approach to the problem of electron correlation. Like standard density functional theory, it contains an unknown exchange-correlation functional, for which several approximations have been proposed in the last years. In this article, we benchmark some of these functionals in an extended set of molecules with respect to total and atomization energies. Our results show that the most recent RDMFT functionals give very satisfactory results compared to more involved quantum chemistry and density functional approaches.Comment: 17 pages, 1 figur