The inverse-square interaction phase diagram: unitarity in the bosonic ground state

Ground-state properties of bosons interacting via inverse square potential (three dimensional Calogero-Sutherland model) are analyzed. A number of quantities scale with the density and can be naturally expressed in units of the Fermi energy and Fermi momentum multiplied by a dimensionless constant (Bertsch parameter). Two analytical approaches are developed: the Bogoliubov theory for weak and the harmonic approximation (HA) for strong interactions. Diffusion Monte Carlo method is used to obtain the ground-state properties in a non-perturbative manner. We report the dependence of the Bertsch parameter on the interaction strength and construct a Pad\'e approximant which fits the numerical data and reproduces correctly the asymptotic limits of weak and strong interactions. We find good agreement with beyond-mean field theory for the energy and the condensate fraction. The pair distribution function and the static structure factor are reported for a number of characteristic interactions. We demonstrate that the system experiences a gas-solid phase transition as a function of the dimensionless interaction strength. A peculiarity of the system is that by changing the density it is not possible to induce the phase transition. We show that the low-lying excitation spectrum contains plasmons in both phases, in agreement with the Bogoliubov and HA theories. Finally, we argue that this model can be interpreted as a realization of the unitary limit of a Bose system with the advantage that the system stays in the genuine ground state contrarily to the metastable state realized in experiments with short-range Bose gases.Comment: published version, 27 pages, 6 figures, 1 tabl

Low-dimensional weakly interacting Bose gases: non-universal equations of state

The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. In the dilute regime the equation of state is universal in terms of the gas parameter, i.e. it is the same for different potentials with the same value of the s-wave scattering length. Series expansions of the universal equation of state are reported for one- and two- dimensional systems. We propose to use the concept of energy-dependent s-wave scattering length for obtaining estimations of non-universal terms in the energy expansion. We test this approach by making a comparison to exactly solvable one-dimensional problems and find that the generated terms have the correct structure. The applicability to two-dimensional systems is analyzed by comparing with results of Monte Carlo simulations. The prediction for the non-universal behavior is qualitatively correct and the densities, at which the deviations from the universal equation of state become visible, are estimated properly. Finally, the possibility of observing the non-universal terms in experiments with trapped gases is also discussed.Comment: 11 pages, 4 figure

Quasiequilibrium supersolid phase of a two-dimensional dipolar crystal

We have studied the possible existence of a supersolid phase of a two-dimensional dipolar crystal using quantum Monte Carlo methods at zero temperature. Our results show that the commensurate solid is not a supersolid in the thermodynamic limit. The presence of vacancies or interstitials turns the solid into a supersolid phase even when a tiny fraction of them are present in a macroscopic system. The effective interaction between vacancies is repulsive making a quasiequilibrium dipolar supersolid possible.Comment: 5 pages, 4 figure

Development of high sensitive real-time PCR to detect mustard and other allergens of the family Brassicaceae in food samples

Mustard is a commonly used condiment including in production of other food products. As mustard is an allergen, it is necessary to control its presence. The development of PCR test-systems for its detection is complicated by the fact that this condiment can be made from seeds of various plant species (Brassica juncea, Brassica nigra, Sinapis alba) of the family Brassicaceae that are not closely related. This family includes other plant species such as white cabbage (Brassica oleracea) and rapeseed (Brassica napus), which can cause the allergic reaction, although seldom. In this connection, many authors use primers specific to many species of this family, including to allergens, to detect mustard. In this work, we used the similar strategy. To increase sensitivity, primers for the mitochondrial COX gene were selected. To increase PCR stability in analysis of deeply processed products, primers were selected for a region with a length of 61 base pair. In the work, the specificity and sensitivity of the developed PCR method was confirmed. Analyses of different products, including those that underwent deep technological processing, were carried out with these primers. Also, primers were selected to detect white mustard (S. alba). When analyzing products on the presence of white mustard, charac‑ teristic regional preferences were demonstrated: this species is used in manufacturing products mainly in the UK and USA