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The theory of atomic Boson-Fermion mixtures in the dilute limit beyond mean-field is considered in this thesis. Extending the formalism of quantum field theory we derived expressions for the quasi-particle excitation spectra, the ground state energy, and related quantities for a homogenous system to first order in the dilute gas parameter. In the framework of density functional theory we could carry over the previous results to inhomogeneous systems. We then determined to density distributions for various parameter values and identified three different phase regions: (i) a stable mixed regime, (ii) a phase separated regime, and (iii) a collapsed regime. We found a significant contribution of exchange-correlation effects in the latter case. Next, we determined the shift of the Bose-Einstein condensation temperature caused by Boson-Fermion interactions in a harmonic trap due to redistribution of the density profiles. We then considered Boson-Fermion mixtures in optical lattices. We calculated the criterion for stability against phase separation, identified the Mott-insulating and superfluid regimes both, analytically within a mean-field calculation, and numerically by virtue of a Gutzwiller Ansatz. We also found new frustrated ground states in the limit of very strong lattices. ----Anmerkung: Der Autor ist Träger des durch die Physikalische Gesellschaft zu Berlin vergebenen Carl-Ramsauer-Preises 2004 für die jeweils beste Dissertation der vier Universitäten Freie Universität Berlin, Humboldt-Universität zu Berlin, Technische Universität Berlin und Universität Potsdam.
We study numerically the behavior of the autocorrelation function (ACF) and the power spectrum of spiral attractors without and in the presence of noise. It is shown that the ACF decays exponentially and has two different time scales. The rate of the ACF decrease is defined by the amplitude fluctuations on small time intervals, i.e., when tau < tau(cor), and by the effective diffusion coefficient of the instantantaneous phase on large time intervals. it is also demonstrated that the ACF in the Poincare map also decreases according to the exponential law exp(-lambda(+)k), where lambda(+) is the positive Lyapunov exponent. The obtained results are compared with the theory of fluctuations for the Van der Pol oscillator
The unification of X-ray and radio selected BL Lacs has been an outstanding problem in the blazar research in the past years. Recent investigations have shown that the gap between the two classes can be filled with intermediate objects and that apparently all differences can be explained by mutual shifts of the peak frequencies of the synchrotron and inverse Compton component of the emission. We study the consequences of this scheme using a new sample of X-ray selected BL Lac objects comprising 104 objects with z<0.9 and a mean redshift bar {z} = 0.34. 77 BL Lacs, of which the redshift could be determined for 64 (83%) objects, form a complete sample. The new data could not confirm our earlier result, drawn from a subsample, that the negative evolution vanishes below a synchrotron peak frequency log nupeak = 16.5. The complete sample shows negative evolution at the 2sigma level (< Ve/Va > = 0.42 +/- 0.04). We conclude that the observed properties of the HRX BL Lac sample show typical behaviour for X-ray selected BL Lacs. They support an evolutionary model, in which flat-spectrum radio quasars (FSRQ) with high energetic jets evolve towards low frequency peaked (mostly radio-selected) BL Lac objects and later on to high frequency peaked (mostly X-ray selected) BL Lacs.