Quantum depletion of collapsing Bose-Einstein condensates

We perform the first numerical three-dimensional studies of quantum field effects in the Bosenova experiment on collapsing condensates by E. Donley et al. [Nature 415, 39 (2002)] using the exact experimental geometry. In a stochastic truncated Wigner simulation of the collapse, the collapse times are larger than the experimentally measured values. We find that a finite temperature initial state leads to an increased creation rate of uncondensed atoms, but not to a reduction of the collapse time. A comparison of the time-dependent Hartree-Fock-Bogoliubov and Wigner methods for the more tractable spherical trap shows excellent agreement between the uncondensed populations. We conclude that the discrepancy between the experimental and theoretical values of the collapse time cannot be explained by Gaussian quantum fluctuations or finite temperature effects.Comment: 9 pages, 4 figures, replaced with published versio

Quantum-field dynamics of expanding and contracting Bose-Einstein condensates

We analyze the dynamics of quantum statistics in a harmonically trapped Bose-Einstein condensate, whose two-body interaction strength is controlled via a Feshbach resonance. From an initially non-interacting coherent state, the quantum field undergoes Kerr squeezing, which can be qualitatively described with a single mode model. To render the effect experimentally accessible, we propose a homodyne scheme, based on two hyperfine components, which converts the quadrature squeezing into number squeezing. The scheme is numerically demonstrated using a two-component Hartree-Fock-Bogoliubov formalism.Comment: 9 pages, 4 figure

Cannabinoid receptors expression in bone marrow trephine biopsy of chronic lymphocytic leukaemia patients treated with purine analogues

Background: Cannabinoid receptors CB1 and CB2 are part the endocannabinoid system that plays an important role in the process of proliferation and apoptosis of different neoplastic cells. B-cell chronic lymphocytic leukaemia is one of the diseases in which these processes are altered. Aim: The aim of our study was the assessment of cannabinoid receptor expression on the B-lymphocytes in bone marrow trephine biopsy from leukaemic patients at diagnosis and after purine analogue treatment. Methods: The biopsy was taken routinely and standard immunohistochemical staining procedure for paraffin embedded sections was applied. The cannabinoid receptors were detected using specific primary polyclonal antibody anti-CB1 and anti-CB2. Additionally, an existence of cannabinoid receptors was confirmed by flow cytometry. Results: The results showed that the expression of CB1 receptor on the surface of neoplastic cells was lower than that of CB2 (17.0 ± 3.1% and 92.1 ± 1.7% respectively, p < 0.001). Nine of the patients responded to applied treatment with a reduction in leukaemic infiltration (77.2 ± 6.9% to 30.2 ± 6.5%, p = 0.007) and CB1 receptor expression (24.4 ± 4.8% to 8.6 ± 2.9%, p = 0.01), but there was no change in CB2 expression (91.7 ± 2.7% vs 90.9 ± 2.8%, p = 0.69). Four patients without remission expressed even greater number of the receptors. In all of the cases both cannabinoid receptor types antibodies gave positive reaction. Furthermore, the existence of cannabinoid receptors on neoplastic lymphocytes was confirmed by flow cytometry. Conclusion: The study provides original evidence for the existence of cannabinoid receptors on B-lymphocytes in chronic lymphocytic leukaemia patients. The receptors are thought to be a new structure that can modify the course of the disease and may be considered as a new target in leukaemia treatment.Обоснование: рецепторы каннабиноидов CB1 и CB2 яв ляются частью системы эндоканнабиноидов, которая играет важную роль в процессах пролиферации и апоптоза различных неопластических клеток. Одним из заболеваний, при которых происходит нарушение этих процессов, является В-клеточный хронический лимфлейкоз. Цель: оценка экспрессии рецепторов каннабиноидов на В-лимфоцитах в трепанобиоптатах у больных лейкозом до и после проведения лечения с использованием пуриновых аналогов. Методы: биоптаты получили рутинными методами; иммуногистохимическое исследование депарафинизированных срезов проводили по стандартной процедуре. Рецепторы каннабиноидов определяли с использованием специфических моноклональных антител анти-CB1 и анти-CB2. Кроме того, наличие рецепторов подтверждено при по- мощи проточной цитофлуориметрии. Результаты: показано, что экспрессия рецептора CB1 на поверхности опухолевых клеток ниже, чем экспрессия CB2 (17,0  ± 3,1% и 92,1 1,7% твенно, p < 0,001). После проведенного лечения у 9 пациентов отмечалось уменьшение лейкозного инфильтрата (77,2 6,9% до 30,2 6,5%, p = 0,007) и снижение экспрессии рецептора CB1 (24,4 4,8% до 8,6 2,9%, p = 0,01), однако различий в экспрессии CB2 не отмечали (91,7 2,7% против 90,9 2,8%, p = 0,69). У 4 пациентов, у которых не удалось достичь ремиссии, определяли даже повышение экспрессии рецепторов. Во всех случаях маркировки антителами к обоим типам рецепторов каннабиноидов отмечали поло- жительную реакцию. Более того, присутствие рецепторов каннабиноидов на злокачественных клетках подтверждали при помощи проточной цитометрии. Выводы: в ходе исследования показано изначальное наличие рецепторов каннабиноидов на В-лимфоцитах у больных хроническим лимфолейкозом. Указанные рецепторы могут быть новой структурой, которая может быть модифицирована в течение болезни, и могут считаться новой мишенью при лечении больных лейкозом

Zipf's law in Multifragmentation

We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent $\tau \simeq 2$. We also recall why the presence of such distribution is not a reliable signal of a liquid-gas phase transition

A search on Dirac equation

The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are discussed in a unified framework and certain solutions of a large class of potentials are given.Comment: 9 page

New Shape Invariant Potentials in Supersymmetric Quantum Mechanics

Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are reflectionless and possess an infinite number of bound states. They can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for energy eigenvalues, eigenfunctions and transmission coefficients are given. Included in our potentials as a special case is the self-similar potential recently discussed by Shabat and Spiridonov.Comment: 8pages, Te

Supersonic optical tunnels for Bose-Einstein condensates

We propose a method for the stabilisation of a stack of parallel vortex rings in a Bose-Einstein condensate. The method makes use of a hollow laser beam containing an optical vortex. Using realistic experimental parameters we demonstrate numerically that our method can stabilise up to 9 vortex rings. Furthermore we point out that the condensate flow through the tunnel formed by the core of the optical vortex can be made supersonic by inserting a laser-generated hump potential. We show that long-living immobile condensate solitons generated in the tunnel exhibit sonic horizons. Finally, we discuss prospects of using these solitons for analogue gravity experiments.Comment: 14 pages, 3 figures, published versio