73,492 research outputs found
Approximating parabolas as natural bounds of Heisenberg spectra: Reply on the comment of O. Waldmann
O. Waldmann has shown that some spin systems, which fulfill the condition of
a weakly homogeneous coupling matrix, have a spectrum whose minimal or maximal
energies are rather poorly approximated by a quadratic dependence on the total
spin quantum number. We comment on this observation and provide the new
argument that, under certain conditions, the approximating parabolas appear as
natural bounds of the spectrum generated by spin coherent states.Comment: 2 pages, accepted for Europhysics Letter
Classification of multidimensional inflationary models
We define under which circumstances two multi-warped product spacetimes can
be considered equivalent and then we classify the spaces of constant curvature
in the Euclidean and Lorentzian signature. For dimension D=2, we get
essentially twelve representations, for D=3 exactly eighteen. More general, for
every even D, 5D+2 cases exist, whereas for every odd D, 5D+3 cases exist. For
every D, exactly one half of them has the Euclidean signature. Our definition
is well suited for the discussion of multidimensional cosmological models, and
our results give a simple algorithm to decide whether a given metric represents
the inflationary de Sitter spacetime (in unusual coordinates) or not.Comment: 21 pages, LaTeX, no figures, J. Math. Phys. in prin
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