Complex wave function, Chiral spin order parameter and Phase Problem

We study the two dimensional Hubbard model by use of the ground state algorithm in the Monte Carlo simulation. We employ complex wave functions as trial function in order to have a close look at properties such as chiral spin order ($\chi$SO) and flux phase. For half filling, a particle-hole transformation leads to sum rules with respect to the Green's functions for a certain choice of a set of wave functions. It is then analytically shown that the sum rules lead to the absence of the $\chi$SO. Upon doping, we are confronted with the sign problem, which in our case %ch appears as a ``phase problem" due to the phase of the Monte Carlo weights. The average of the phase shows an exponential decay as a function of inverse temperature similarly to that of sign by Loh Jr. et. al. . We compare the numerical results with those of exact numerical calculations.Comment: 28 pages, 9 figures(hard copy will be available upon request

Interference between a large number of independent Bose-Einstein condensates

We study theoretically the interference patterns produced by the overlap of an array of Bose-Einstein condensates that have no phase coherence among them. We show that density-density correlations at different quasimomenta, which play an important role in two-condensate interference, become negligible for large $N$, where $N$ is the number of overlapping condensates. In order to understand the physics of this phenomenon, it is sufficient to consider the periodicity of the lattice and the statistical probability distribution of a random-walk problem. The average visibility of such interference patterns decreases as $N^{-1/2}$ for large $N$.Comment: 9 pages, 2 figure

Remote sensing of water quality in reservoirs and lakes in semi-arid climates

Overlake measurements using aerial cameras (remote sensing) combined with water truth collected from boats most economically provided wide-band photographs rather than precise spectra. With use of false color infrared film (400-950 nm), the reflected spectral signatures seen from hundreds to thousands of meters above the lake merged to produce various color tones. Such colors were easily and inexpensively obtained and could be recognized by lake management personnel without any prior training. The characteristic spectral signatures of various algal types were also recognizable in part by the color tone produced by remote sensing

Shaping an ultracold atomic soliton in a travelling wave laser beam

An ultracold wave packet of bosonic atoms loaded into a travelling laser wave may form a many-atom soliton.This is disturbed by a homogeneous force field, for example by the inevitable gravitation. The wave packet is accelerated and therefore the laser frequency appears to be chirped in the rest frame of the atoms. We derive the effective nonlinear Schr\"odinger equation. It shows a time dependent nonlinearity coefficient which amounts to a damping or antidamping, respectively. The accelerated packet solution remains a soliton which changes its shape adiabatically. Similarly, an active shaping can be obtained in the force-free case by chirping the laser frequency thus representing a way of coherent control of the soliton form. The experimental consequences are discussed.Comment: 5 pages, Latex, to published in Europhys. Let

A PRELIMINARY REVIEW OF THE BIOSTRATIGRAPHY OF THE UPPERMOST PERMIAN, TRIASSIC AND LOWERMOST JURASSIC OF GONDWANALAND

This review pager was born out of a desire to visualize in some detail the picture of the evolving Gondwana Triassic landscape and the story of life and ecology upon it; a desire to provide a general setting in which to view the details of the work in which we are actively involved at the present-the macro flora (H.M.A.) and microflora (J.M.A.) of the Molteno 'Formation' of the Karroo Basin of South Africa