Stability of spherically trapped three-dimensional Bose-Einstein condensates against macroscopic fragmentation

We consider spherically trapped Bose gases in three dimensions with contact interactions and investigate whether the Bose-Einstein condensate at zero temperature is stable against macroscopic fragmentation into a small number of mutually incoherent pieces. Our results are expressed in terms of a dimensionless interaction measure proportional to the Thomas-Fermi parameter. It is shown that while three-dimensional condensates are inherently much more stable against macroscopic fragmentation than their quasi-one-and quasi-two-dimensional counterparts, they fragment at a sufficiently large value of the dimensionless interaction measure, which we determine both fully numerically and semianalytically from a continuum limit of large particle numbersU.R.F. was supported by the NRF Korea (Grants No. 2010-0013103 and No. 2011-0029541) and the Seoul National University Foundation Research Expense. P. B. received support from the Ministerio de Ciencia e Innovacion of Spain under Projects No. MTM2009-08587 and No. MTM2010-18246-C03 and a FPU fellowship through Grant No. AP2009-1892.Bader, PKH.; Fischer, U. (2013). Stability of spherically trapped three-dimensional Bose-Einstein condensates against macroscopic fragmentation. Physical Review A. 87(2):23632-23632. https://doi.org/10.1103/PhysRevA.87.023632236322363287

Observer dependence for the phonon content of the sound field living on the effective curved space-time background of a Bose-Einstein condensate

We demonstrate that the ambiguity of the particle content for quantum fields in a generally curved space-time can be experimentally investigated in an ultracold gas of atoms forming a Bose-Einstein condensate. We explicitly evaluate the response of a suitable condensed matter detector, an ``Atomic Quantum Dot,'' which can be tuned to measure time intervals associated to different effective acoustic space-times. It is found that the detector response related to laboratory, ``adiabatic,'' and de Sitter time intervals is finite in time and nonstationary, vanishing, and thermal, respectively.Comment: 9 pages, 2 figures; references updated, as published in Physical Review

On the theory of vortex quantum tunnelling in the dense Bose superfluid helium II

The quantum tunnelling and nucleation theory of vortices in helium II is reviewed. Arguments are given that the only reliable method to calculate tunnelling probabilities in this highly correlated, strongly interacting many-body system is the semiclassical, large scale approach for evaluation of the tunnelling exponent, which does not make any assumptions about the unknown dynamical behaviour of the fluid on microscopic scales. The geometric implications of this semiclassical theory are represented in some detail and its relevance for the interpretation of experimental data is discussed.Comment: 25 pages, 6 figures, revised version, to appear in Physica

Relativistic Kinetics of Phonon Gas in Superfluids

The relativistic kinetic theory of the phonon gas in superfluids is developed. The technique of the derivation of macroscopic balance equations from microscopic equations of motion for individual particles is applied to an ensemble of quasi-particles. The necessary expressions are constructed in terms of a Hamilton function of a (quasi-)particle. A phonon contribution into superfluid dynamic parameters is obtained from energy-momentum balance equations for the phonon gas together with the conservation law for superfluids as a whole. Relations between dynamic flows being in agreement with results of relativistic hydrodynamic consideration are found. Based on the kinetic approach a problem of relativistic variation of the speed of sound under phonon influence at low temperature is solved.Comment: 23 pages, Revtex fil

Methods for direct determination of mitomycin C in aqueous solutions and in urine

Stripping voltammetry (SV) is used to quantitatively determine concentrations of the anti-neoplastic drug mitomycin C (MMC) alone and in mixtures with 5-fluorouracil and cisplatin, both of which are used in combined chemotherapy with MMC. If the accumulation is performed at the potentials of MMC reduction (-0.35 V vs. SCE), reduced MMC is strongly adsorbed at the electrode. It is possible to prepare a MMC-modified electrode, which, after a washing step, is transferred to the background electrolyte to determine MMC by voltammetry. This procedure, which is termed transfer stripping voltammetry (TSV), helps to eliminate interferences and can be applied for a direct determination of MMC alone or in mixtures with other drugs in urine

Oscillations of a rapidly rotating annular Bose-Einstein condensate

A time-dependent variational Lagrangian analysis based on the Gross-Pitaevskii energy functional serves to study the dynamics of a metastable giant vortex in a rapidly rotating Bose-Einstein condensate. The resulting oscillation frequencies of the core radius reproduce the trends seen in recent experiments [Engels et al., Phys. Rev. Lett. 90, 170405 (2003)], but the theoretical values are smaller by a factor approximately 0.6-0.8.Comment: 7 pages, revtex

The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate

We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. Writing the coupling parameter as 1 / \eps^2 we consider the asymptotic regime \eps \to 0 with the angular velocity $\Omega$ proportional to (\eps^2|\log\eps|)^{-1} . We prove that if \Omega = \Omega_0 (\eps^2|\log\eps|)^{-1} and $\Omega_0 > 2(3\pi)^{-1}$ then a minimizer of the GP energy functional has no zeros in an annulus at the boundary of the disc that contains the bulk of the mass. The vorticity resides in a complementary `hole' around the center where the density is vanishingly small. Moreover, we prove a lower bound to the ground state energy that matches, up to small errors, the upper bound obtained from an optimal giant vortex trial function, and also that the winding number of a GP minimizer around the disc is in accord with the phase of this trial function.Comment: 52 pages, PDFLaTex. Minor corrections, sign convention modified. To be published in Commun. Math. Phy

The TF Limit for Rapidly Rotating Bose Gases in Anharmonic Traps

Starting from the full many body Hamiltonian we derive the leading order energy and density asymptotics for the ground state of a dilute, rotating Bose gas in an anharmonic trap in the ` Thomas Fermi' (TF) limit when the Gross-Pitaevskii coupling parameter and/or the rotation velocity tend to infinity. Although the many-body wave function is expected to have a complicated phase, the leading order contribution to the energy can be computed by minimizing a simple functional of the density alone