15,539 research outputs found
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
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