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

Practical thermodynamics of Yukawa systems at strong coupling

Simple practical approach to estimate thermodynamic properties of strongly coupled Yukawa systems, in both fluid and solid phases, is presented. The accuracy of the approach is tested by extensive comparison with direct computer simulation results (for fluids and solids) and the recently proposed shortest-graph method (for solids). Possible applications to other systems of softly repulsive particles are briefly discussed.Comment: Published in J. Chem. Phy

Scanning Electron Microscopy Study of Drilling Cuttings in Tomsk Oblast Sites

The research is focused on determining mineralogical composition of drilling cuttings by scanning electron microscope as well as imaging the sample surface of high resolution that allows studying the structural characteristics of the site. In addition, a number of other techniques permit obtaining information on chemical composition of sample in near-surface layers. The study in drilling cuttings by means of scanning microscopy has revealed the presence of titanium, iron, zirconium oxides, iron sulphide, barium sulphate. The former is a mineral that concentrates rare-earth elements, presumably monocyte, as well as uranium silicate, etc. The results obtained confirm the data of previous X-ray structural analysis, i.e. the study samples consist of alumosilicate matrix. Apart from silicon and aluminium oxides, the matrix includes such elements as Na, K, Mg. Such a composition corresponds to rock-forming minerals: quartz, albite, microcline, clinochlore, muscovite, anorthoclase

Mucin-poor mucinous tubular and spindle cell kidney cancer and clear cell renal cell carcinoma: a rare clinical case

Mucinous tubular and spindle cell carcinoma of the kidney is a rare low-grade malignant tumour and accounts for less than 1% of all renal neoplasms. The classic morphological structure of the tumor is represented by three elements: spindle cells, ducts and myxoid or mucinous stroma. This tumor is indolent with a low risk of metastasis and a favorable outcome. However, cases with relapses, metastases to regional lymph nodes, and distant metastases, which were mainly characterised by high nuclear atypia, sarcomatoid transformation and other atypical morphological features are described in the literature. Several cases of mucin-poor and mucin-free mucinous tubular and spindle cell renal cell carcinoma have also been presented, making it difficult to differentiate from other renal cell carcinomas. There are reports of cases of mucin poor mucinous tubular and spindle cell carcinoma, which were accompanied by relapses and metastases. Thus, although the tumour is indolent, careful follow-up is necessary even after radical excision. In this article, we report a rare clinical case of combination of mucin-poor mucinous tubular and spindle cell carcinoma and clear cell renal cell carcinoma of the kidney in a 50-year-old man. The results of clinical and instrumental studies, as well as the morphological features of both tumors are presented. Due to the atypical morphological structure of mucinous tubular and spindle cell carcinoma, the final diagnosis was possible using an immunohistochemical method, which demonstrated the immunohistochemical profile characteristic of this tumour

The Minimum-Uncertainty Squeezed States for for Atoms and Photons in a Cavity

We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions. The corresponding photons statistics are discussed and some applications to quantum optics, cavity quantum electrodynamics, and superfocusing in channeling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.Comment: 27 pages, no figures, 174 references J. Phys. B: At. Mol. Opt. Phys., Special Issue celebrating the 20th anniversary of quantum state engineering (R. Blatt, A. Lvovsky, and G. Milburn, Guest Editors), May 201