Convergence to equilibrium under a random Hamiltonian

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.Comment: 11 pages, 1 figure, v1-v3: some minor errors and typos corrected and new references added; v4: results for the degenerated spectrum added; v5: reorganized and rewritten version; to appear in PR

Threat of allergenic airborne grass pollen in Szczecin, NW Poland: the dynamics of pollen seasons, effect of meteorological variables and air pollution

The dynamics of Poaceae pollen season, in particularly that of the Secale genus, in Szczecin (western Poland) 2004–2008 was analysed to establish a relationship between the meteorological variables, air pollution and the pollen count of the taxa studied. Consecutive phases during the pollen season were defined for each taxon (1, 2.5, 5, 25, 50, 75, 95, 97.5, 99% of annual total), and duration of the season was determined using the 98% method. On the basis of this analysis, the temporary differences in the dynamics of the seasons were most evident for Secale in 2005 and 2006 with the longest main pollen season (90% total pollen). The pollen season of Poaceae started the earliest in 2007, when thermal conditions were the most favourable. Correlation analysis with meteorological factors demonstrated that the relative humidity, mean and maximum air temperature, and rainfall were the factors influencing the average daily pollen concentrations in the atmosphere; also, the presence of air pollutants such as ozone, PM10 and SO2 was statistically related to the pollen count in the air. However, multiple regression models explained little part of the total variance. Atmospheric pollution induces aggravation of symptoms of grass pollen allergy