Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 03/05

Since Markowitz in 1952 described an efficient and practical way of finding the optimal portfolio allocation in the normal distributed case, a lot of progress in several directions has been made. The main objective of this thesis is to replace the original risk measure of the Markowitz setting by a more suitable one, Value-at-Risk. In adressing the optimal allocation problem in a slightly more general setting, thereby still allowing for a large number of different asset classes, an efficient algorithm is developed for finding the exact solution in the case of specially distributed losses. Applying this algorithm to even more general loss distributions results in a not necessarily exact matching of the VaR optimum. However, in this case, upper bounds for the euclidean distance between the exact optimum and the output of the proposed algorithm are given. An investigation of these upper bounds shows, that in general the algorithm results in quite good approximations to the VaR optimum. Finally, an application of a stochastic branch & bound algorithm to the current problem is discussed.

The generation of coherent high-order harmonics from the interaction of ultra-intense femtosecond laser pulses with solid density plasmas holds the promise for table-top sources of intense extreme ultraviolet (XUV) and soft x-ray (SXR) radiation. Furthermore, they give rise to the prospect of combining the attosecond pulse duration of conventional gas-harmonic sources with the photon flux currently only available from large-scale free-electron

laser or synchrotron facilities.

In this thesis a series of experiments studying various aspects of harmonic generation from such a plasma source are presented and the emitted XUV-radiation is characterized

spectrally, spatially and temporally. The measurements probe the dynamics of the plasma surface on a sub-laser-cycle time scale and help to increase our understanding of the harmonic generation process. It is shown that, at moderate intensities and laser contrast,

the emitted harmonics are indeed phase-locked but chirped and emitted as a train of XUV-bursts of attosecond duration. Measurements with very high contrast relativistically intense driving pulses reveal the generation of harmonics up to the relativistic cutoff in

a diffraction-limited beam with constant divergence observed for all wavelength. This implies that the harmonics are generated on a curved surface and travel through a focus after the target possibly opening a route towards extreme intensities in the process. In addition it is found that a target roughness on the scale of the wavelength of the highest generated harmonic does not adversely affect the harmonic beam quality implying that

the generation of diffraction-limited keV-harmonic beams should be possible. In a third set of experiments the first demonstration of harmonic generation from solid targets using an 8 fs driving laser opens a route towards the generation of ultra-intense single-as pulses and gives conclusive evidence for the unequal spacing of the harmonic emission.

Based on these results the development of ultra-intense sources of single as-pulses from the interaction of intense laser pulses with solid surfaces could advance at a fast pace making XUV-pump XUV-probe type investigations of nonlinear processes with attosecond time resolution feasible in the near future.

This thesis presents a study of the near-IR spectral properties of six globular clusters (GCs) and 21 early-type galaxies in the local Universe, 10 of which are in low density environments and 11 are in the Fornax cluster of galaxies. Our observations were acquired using integral field unit (IFU) and long-slit spectrographs. The common goal of the various projects was to verify the predictions of current stellar population models in the near-IR using GCs and early-type galaxies data. We provide the first spectral library of the integrated near-IR light of globular clusters with ages > 1 Gyr.

Using VLT/SINFONI we obtained integrated luminosity weighted spectra of six GCs in the Large Magellanic Cloud (LMC). Three of them are old > 10 Gyr) and metal poor ([Z/H]~-1.4), the other three have intermediate ages (1< age < 3 Gyr) and higher metallicity ([Z/H]~-0.4). We have measured the strength of the near-IR K-band features Na I, Ca I and 12CO(2-0) and compared the Dco index, used to measure the strength of 12CO(2-0), with the predictions of the stellar population models of Maraston (2005). We find reasonable agreement between the data and the model predictions for old and metal poor GCs. For intermediate age and half solar metallicity GCs we find a marked disagreement with the models. While the models predict an increase of the index with younger ages, we find a strong drop of index strength at ~1 Gyr. We consider that

this is due to the different spectral properties of galactic carbon rich AGB stars, used to empirically calibrate the models, and the ones present in LMC globular clusters. This conclusion is based on the different Dco index strength that we measure for the carbon stars in our LMC sample and the galactic carbon stars for a given (J-K)

colour.

Our study of early-type galaxies in low density environments and in the Fornax cluster reveals that the near-IR Na I and Dco indices follow similar index-sigma scaling relations as optical metallicity indices. The Na I index shows a good positive correlation with the metallicity at old ages and additionally increases for younger ages in contrast to the behaviour of optical metal indices. We derive an empirical calibration for the Na I index as function of metallicity and suggest that a diagnostic diagram, based on the optical hydrogen Balmer

index and the near-IR Na I index, will be a good age-metallicity estimator once more detailed SSP models in the near-IR become available. The Dco index exhibits similar trends with metallicity, albeit with a shallower slope and more complex behaviour at young ages. We find evidence of saturation of the Dco index above twice

solar metallicity.

Utilising the superb spatial resolution of adaptive optics assisted IFU observations in the near-IR we observed the centre of the Fornax cD galaxy NGC 1399. We confirm the presence of a central velocity dispersion drop within r<0.2" and reveal drops in the Na I and Dco index with the same extent and location. We suggest that the centre of NGC 1399 harbours a cold subsystem with a distinct stellar population, which is either more metal poor, or younger and

more metal poor than the main body of the galaxy. We detect a negative gradient of the Na I index within r<1.4". Using our calibration of Na I vs. metallicity we derive a metallicity gradient, which appears to be shallower than the typical metallicity gradients measured at larger radii in other early-type galaxies.