Comment on "Bounding and approximating parabolas for the spectrum of Heisenberg spin systems" by Schmidt, Schnack and Luban

Recently, Schmidt et al. proved that the energy spectrum of a Heisenberg spin system (HSS) is bounded by two parabolas, i.e. lines which depend on the total spin quantum number S as S(S+1). The prove holds for homonuclear HSSs which fulfill a weak homogenity condition. Moreover, the extremal values of the exact spectrum of various HSS which were studied numerically were found to lie on approximate parabolas, named rotational bands, which could be obtained by a shift of the boundary parabolas. In view of this, it has been claimed that the rotational band structure (RBS) of the energy spectrum is a general behavior of HSSs. Furthermore, since the approximate parabolas are very close to the true boundaries of the spectrum for the examples discussed, it has been claimed that the methods allow to predict the detailed shape of the spectrum and related properties for a general HSS. In this comment I will show by means of examples that the RBS hypothesis is not valid for general HSSs. In particular, weak homogenity is neither a necessary nor a sufficient condition for a HSS to exhibit a spectrum with RBS.Comment: Comments on the work of Schmidt et al, Europhys. Lett. 55, 105 (2001), cond-mat/0101228 (for the reply see cond-mat/0111581). To be published in Europhys. Let

Balance training of the equilibrium organ and its effect on flight strategy

An experimental program was conducted with the pendular platform of the Oto-Rhino-Laryngology Clinic, which was developed for the investigation of disturbances of the equilibrium. The equilibrium sense of the glider pilot was emphasized. Results are presented

Localized spectral asymptotics for boundary value problems and correlation effects in the free Fermi gas in general domains

We rigorously derive explicit formulae for the pair correlation function of the ground state of the free Fermi gas in the thermodynamic limit for general geometries of the macroscopic regions occupied by the particles and arbitrary dimension. As a consequence we also establish the asymptotic validity of the local density approximation for the corresponding exchange energy. At constant density these formulae are universal and do not depend on the geometry of the underlying macroscopic domain. In order to identify the correlation effects in the thermodynamic limit, we prove a local Weyl law for the spectral asymptotics of the Laplacian for certain quantum observables which are themselves dependent on a small parameter under very general boundary conditions

Environmental charging tests of spacecraft thermal control louvers

The environmental charging of spacecraft surfaces program consists, in part, of experimental evaluation of material response to the environmental charged particle flux. A flight type spacecraft thermal control louver assembly has been tested in an electron flux. The louver blade surface potential, the louver assembly currents, and the relatively high number of discharges observed in the electron environment are self-consistent results. The unexpected result of this testing was the flutter observed when the louvers were closed. The flutter is about 1 to 2 Hz in frequency and is probably electrostatically induced