Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions

We consider an interacting homogeneous Bose gas at zero temperature in two spatial dimensions. The properties of the system can be calculated as an expansion in powers of g, where g is the coupling constant. We calculate the ground state pressure and the ground state energy density to second order in the quantum loop expansion. The renormalization group is used to sum up leading and subleading logarithms from all orders in perturbation theory. In the dilute limit, the renormalization group improved pressure and energy density are expansions in powers of the T ^2B and T ^2Bln(T ^2B), respectively, where T ^2B is the two-body T-matrix. Received 19 April 2002 Published online 13 August 2002     

Quantum information processing in optical images

Optical images can be used to transport, store and process information in a parallel way. We discuss different results obtained in the domain of ‘quantum imaging’, aiming at exploiting at the same time the quantum properties of optical images and their intrinsic parallelism. We define the notion of standard quantum limit (SQL) in optical resolution, set by the quantum noise of usual coherent light, and show that it can be much lower than the diffraction limit. We also prove that this limit can be circumvented by especially designed nonclassical and multimode light. We present an experiment showing that OPOs oscillating inside an exactly confocal cavity actually produce such transverse multimode nonclassical light. We finally describe another experiment which has surpassed the SQL in the case of beam positioning, both in the 1D and 2D cases.     

Rückbezüge des Mathematikunterrichts und der Methodik des Mathematikunterrichts in der DDR auf historische Vorausentwicklungen

The author discusses at some examples exemplarily, how the pedagogy of mathematics education in the GDR from curricular and educational/psychological knowledge from the time before 1945 has developed scientifically.