The bilinear-biquadratic model on the complete graph

We study the spin-1 bilinear-biquadratic model on the complete graph of N sites, i.e., when each spin is interacting with every other spin with the same strength. Because of its complete permutation invariance, this Hamiltonian can be rewritten as the linear combination of the quadratic Casimir operators of su(3) and su(2). Using group representation theory, we explicitly diagonalize the Hamiltonian and map out the ground-state phase diagram of the model. Furthermore, the complete energy spectrum, with degeneracies, is obtained analytically for any number of sites

Bevezetés a talajtanba környezettanosoknak

E jegyzet az ELTE TTK Környezettudomány alapszak Talajtan kurzus hallgatóinak készült, ezért a „klasszikus”, Stefanovits professzor által jegyzett Talajtan-nál jóval szűkebb területet fog át, címéből fakadóan csak bevezeti az olvasót e tudományba. A jegyzet kilenc fejezetben tekinti át a talajok a talajok morfológiai és anyagi felépítését, azok fizikai és kémiai tulajdonságait, a bennük lejátszódó fizikai és kémiai folyamatokat, illetve keletkezésük és folyamatosan zajló átalakulásuk mechanizmusait. Külön fejezet tárgyalja a globálisan jellemző talajok földrajzi helyzetét és fejlődésük főbb mozgató rugóit. A természettudományos megközelítés mellett a jegyzet érinti a talajérték meghatározásának közgazdasági problematikáját is

A review on sheet erosion measurements in Hungary

Soil erosion has a significant role in ecology, economy and in environmental protection therefore its quantification and prediction are very important, particul arly on a national level. Although some details can be described using physical equations, the entire soil erosion process is rather complicated and can be determined only empirically, which requires large measured datasets. Because plot measurement is the most convenient and therefore the most popular way of capturing erosion data, we used plot measurement to understand erosion in Hungary. The northern and the western parts of the country are endangered by sheet erosion, which is why the plots were carried out in those areas. Most of the plots were constructed to determin e the “K” factor of the USLE (Universal Soil Loss Equation) under permanently tilled soils without vegetation cover. Additionally the soil protection effect of various field crops and the additiona l land use types (forest, pasture) was measured in the plots. Furthermore descriptive investigations, rainfall si mulations and soil tracer detections were also used to quantify sheet erosion at different environmental conditions and scales. Despite the large amount of measured data collected, only a few of them have since been pub lished. Due to a lack of available data, national erosion research, erosion prediction, and model calibration are less precise and effective Scaling problems among the measured levels also emphasized a de finite need for a larger and more accessible national database. Finally, without the financial base of additional plot measurements , the publication of the previously gathered data is absolutely necessary to continue soil erosion studies in Hungary