Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

Chemical characterization of oligosaccharides in the milk of six species of New and Old World monkeys.

Human and great ape milks contain a diverse array of milk oligosaccharides, but little is known about the milk oligosaccharides of other primates, and how they differ among taxa. Neutral and acidic oligosaccharides were isolated from the milk of three species of Old World or catarrhine monkeys (Cercopithecidae: rhesus macaque (Macaca mulatta), toque macaque (Macaca sinica) and Hamadryas baboon (Papio hamadryas)) and three of New World or platyrrhine monkeys (Cebidae: tufted capuchin (Cebus apella) and Bolivian squirrel monkey (Saimiri boliviensis); Atelidae: mantled howler (Alouatta palliata)). The milks of these species contained 6-8% total sugar, most of which was lactose: the estimated ratio of oligosaccharides to lactose in Old World monkeys (1:4 to 1:6) was greater than in New World monkeys (1:12 to 1:23). The chemical structures of the oligosaccharides were determined mainly by (1)H-NMR spectroscopy. Oligosaccharides containing the type II unit (Gal(β1-4)GlcNAc) were found in the milk of the rhesus macaque, toque macaque, Hamadryas baboon and tufted capuchin, but oligosaccharides containing the type I unit (Gal(β1-3)GlcNAc), which have been found in human and many great ape milks, were absent from the milk of all species studied. Oligosaccharides containing Lewis x (Gal(β1-4)[Fuc(α1-3)]GlcNAc) and 3-fucosyl lactose (3-FL, Gal(β1-4)[Fuc(α1-3)]Glc) were found in the milk of the three cercopithecid monkey species, while 2-fucosyl lactose (5'-FL, Fuc(α1-2)Gal(β1-4)Glc) was absent from all species studied. All of these milks contained acidic oligosaccharides that had N-acetylneuraminic acid as part of their structures, but did not contain oligosaccharides that had N-glycolylneuraminic acid, in contrast to the milk or colostrum of great apes which contain both types of acidic oligosaccharides. Two GalNAc-containing oligosaccharides, lactose 3'-O-sulfate and lacto-N-novopentaose I (Gal(β1-3)[Gal(β1-4)GlcNAc(β1-6)]Gal(β1-4)Glc) were found only in the milk of rhesus macaque, hamadryas baboon and tufted capuchin, respectively. Further research is needed to determine the extent to which the milk oligosaccharide patterns observed among these taxa represent wider phylogenetic trends among primates and how much variation occurs among individuals or species.