Persistent currents in a bosonic mixture in the ring geometry

In this paper we analyze the possibility of persistent currents of a two-species bosonic mixture in the one-dimensional ring geometry. We extend the arguments used by Bloch to obtain a criterion for the stability of persistent currents for the two-species system. If the mass ratio of the two species is a rational number, persistent currents can be stable at multiples of a certain total angular momenta. We show that the Bloch criterion can also be viewed as a Landau criterion involving the elementary excitations of the system. Our analysis reveals that persistent currents at higher angular momenta are more stable for the two-species system than previously thought.Comment: 20 pages and 7 figure

АНАЛІТИЧНІ ПРОЦЕДУРИ АУДИТУ В УМОВАХ ПІДВИЩЕННЯ ВИМОГ ДО КОНТРОЛЮ ЙОГО ЯКОСТІ

. Under the current conditions of economic development, it is important for owners and shareholders to obtain an independent expert assessment of the effectiveness of the entity’s business. In connection with this, there is a need for wider application of analytical procedures in the audit. In the article the essence, levels and types of analytical procedures of audit are examined, peculiarities of application of analytical procedures during audit in the current conditions of development of the economy of Ukraine are determined. The necessity of improvement of analytical procedures of audit in conditions of increase of requirements to control its quality is substantiated. The shortcomings of estimation of financial stability of the enterprise are determined. In addition, the financial stability of the entity is determined by comparing the actual and optimal values (criteria) of the respective coefficients. The criteria used in programs are generalized and do not take into account the industry and the specifics of the enterprise. Such an assessment of financial stability in many cases does not actually reflect the actual situation on the subject of management. This is due to the fact that the majority of relative indicators of financial stability are determined by the ratio of own and attracted capital, while not taking into account their structure and peculiarities of formation. In addition, the financial stability of an entity is determined by comparing the actual and optimal values (criteria) of the respective coefficients. The criteria used in these programs are generalized and do not take into account the industry and the specifics of the entity’s activities. When applying modern information technology in the audit, we must carefully approach the choice of software products and the final interpretation of the results. In the article proposes a refined and expanded list of optimal values (criteria) of indicators of financial stability, taking into account the specifics of different branches of the national economy. An auditor in assessing the financial sustainability of a business entity — the customer, it is also advisable to take into account the features of his activity and, depending on this, adjust the criteria. To improve the quality of the audit, the use of analytical procedures should be adequate to the objectives and objectives of the audit, and the costs of their conduct should be correlated with the results obtained.Исследованы сущность, уровни и виды аналитических процедур аудита, определены особенности применения аналитических процедур при проведении аудита в современных условиях развития экономики Украины. Обоснована необходимость совершенствования аналитических процедур аудита в условиях повышения требований к контролю его качества. Определены недостатки оценки финансовой устойчивости предприятия — заказчика аудиторских услуг с помощью специализированных программных продуктов. Уточнен и расширен перечень оптимальных значений (критериев) показателей финансовой устойчивости с учетом специфики различных отраслей национальной экономики.За сучасних умов розвитку економіки власникам та акціонерам важливо отримати незалежну експертну оцінку щодо ефективності діяльності суб’єкта господарювання. У зв’язку з цим виникає необхідність більш широкого застосування в аудиті аналітичних процедур. Досліджено сутність, рівні та види аналітичних процедур аудиту, визначено особливості застосування аналітичних процедур при проведенні аудиту в сучасних умовах розвитку економіки України. Обґрунтовано необхідність удосконалення аналітичних процедур аудиту в умовах підвищення вимог до контролю його якості. Визначено недоліки оцінки фінансової стійкості суб’єкта господарювання — замовника аудиторських послуг за допомогою спеціалізованих програмних продуктів. Така оцінка фінансової стійкості здебільшого фактично не відображає реальної ситуації на суб’єкті господарювання. Це зумовлено тим, що більшість відносних показників фінансової стійкості визначаються співвідношенням власного і залученого капіталу, при цьому не враховуються їхні структура та особливості формування. Крім того, фінансову стійкість суб’єкта господарювання визначають порівнянням фактичних і оптимальних значень (критеріїв) відповідних коефіцієнтів. Критерії, які використовуються в цих програмах, є узагальненими і не враховують галузі та специфіки діяльності суб’єкта господарювання. При застосуванні сучасних інформаційних технологій в аудиті необхідно зважено підходити до вибору програмних продуктів і кінцевої інтерпретації отриманих результатів. Запропоновано уточнений і розширений перелік оптимальних значень (критеріїв) показників фінансової стійкості з урахуванням специфіки різних галузей національної економіки. Аудиторові при оцінці фінансової стійкості суб’єкта господарювання — замовника доцільно також ураховувати особливості його діяльності і залежно від цього коригувати критерії. Для підвищення якості аудиторської перевірки застосування аналітичних процедур має бути адекватним завданням і цілям аудиту, а витрати на їх проведення повинні корелюватись з отриманими результатами

Finite temperature excitations of a trapped Bose gas

We present a detailed study of the temperature dependence of the condensate and noncondensate density profiles of a Bose-condensed gas in a parabolic trap. These quantitites are calculated self-consistently using the Hartree-Fock-Bogoliubov equations within the Popov approximation. Below the Bose-Einstein transition the excitation frequencies have a realtively weak temperature dependence even though the condensate is strongly depleted. As the condensate density goes to zero through the transition, the excitation frequencies are strongly affected and approach the frequencies of a noninteracting gas in the high temperature limit.Comment: 4 pages, Latex, 4 postscript figures. Submitted to Physical Review Letter

Excitation spectrum in a cylindrical Bose-Einstein gas

Whole excitation spectrum is calculated within the Popov approximation of the Bogoliubov theory for a cylindrical symmetric Bose-Einstein gas trapped radially by a harmonic potential. The full dispersion relation and its temperature dependence of the zero sound mode propagating along the axial direction are evaluated in a self-consistent manner. The sound velocity is shown to depend not only on the peak density, but also on the axial area density. Recent sound velocity experiment on Na atom gas is discussed in light of the present theory.Comment: 4 pages, 5 eps figure

Landau-Khalatnikov two-fluid hydrodynamics of a trapped Bose gas

Starting from the quantum kinetic equation for the non-condensate atoms and the generalized Gross-Pitaevskii equation for the condensate, we derive the two-fluid hydrodynamic equations of a trapped Bose gas at finite temperatures. We follow the standard Chapman-Enskog procedure, starting from a solution of the kinetic equation corresponding to the complete local equilibrium between the condensate and the non-condensate components. Our hydrodynamic equations are shown to reduce to a form identical to the well-known Landau-Khalatnikov two-fluid equations, with hydrodynamic damping due to the deviation from local equilibrium. The deviation from local equilibrium within the thermal cloud gives rise to dissipation associated with shear viscosity and thermal conduction. In addition, we show that effects due to the deviation from the diffusive local equilibrium between the condensate and the non-condensate (recently considered by Zaremba, Nikuni and Griffin) can be described by four frequency-dependent second viscosity transport coefficients. We also derive explicit formulas for all the transport coefficients. These results are used to introduce two new characteristic relaxation times associated with hydrodynamic damping. These relaxation times give the rate at which local equilibrium is reached and hence determine whether one is in the two-fluid hydrodynamic region.Comment: 26 pages, 3 postscript figures, submitted to PR

Sound propagation in a cylindrical Bose-condensed gas

We study the normal modes of a cylindrical Bose condensate at $T = 0$ using the linearized time-dependent Gross-Pitaevskii equation in the Thomas-Fermi limit. These modes are relevant to the recent observation of pulse propagation in long, cigar-shaped traps. We find that pulses generated in a cylindrical condensate propagate with little spread at a speed $c = \sqrt{g\bar n /m}$, where $\bar n$ is the average density of the condensate over its cross-sectional area.Comment: 4 pages, 2 Postscript figure

Bogoliubov sound speed in periodically modulated Bose-Einstein condensates

We study the Bogoliubov excitations of a Bose-condensed gas in an optical lattice. Of primary interest is the long wavelength phonon dispersion for both current-free and current-carrying condensates. We obtain the dispersion relation by carrying out a systematic expansion of the Bogoliubov equations in powers of the phonon wave vector. Our result for the current-carrying case agrees with the one recently obtained by means of a hydrodynamic theory.Comment: 16 pages, no figure

Bragg spectroscopy of a cigar shaped Bose condensate in optical lattices

We study properties of excited states of an array of weakly coupled quasi-two-dimensional Bose condensates by using the hydrodynamic theory. We calculate multibranch Bogoliubov-Bloch spectrums and its corresponding eigenfunctions. The spectrum of the axial excited states and its eigenfunctions strongly depends on the coupling among various discrete radial modes within a given symmetry. This mode coupling is due to the presence of radial trapping potential. The multibranch nature of the Bogoliubov-Bloch spectrum and its dependence on the mode-coupling can be realized by analyzing dynamic structure factor and momentum transferred to the system in Bragg spectroscopy experiments. We also study dynamic structure factor and momentum transferred to the condensate due to the Bragg spectroscopy experiment.Comment: 7 pages, 5 figures, to appear in Journal of Physics B: Atomic, Molecular & Optical Physic

Mean-Field vs Monte-Carlo equation of state for the expansion of a Fermi superfluid in the BCS-BEC crossover

The equation of state (EOS) of a Fermi superfluid is investigated in the BCS-BEC crossover at zero temperature. We discuss the EOS based on Monte-Carlo (MC) data and asymptotic expansions and the EOS derived from the extended BCS (EBCS) mean-field theory. Then we introduce a time-dependent density functional, based on the bulk EOS and Landau's superfluid hydrodynamics with a von Weizs\"acker-type correction, to study the free expansion of the Fermi superfluid. We calculate the aspect ratio and the released energy of the expanding Fermi cloud showing that MC EOS and EBCS EOS are both compatible with the available experimental data of $^6$Li atoms. We find that the released energy satisfies an approximate analytical formula that is quite accurate in the BEC regime. For an anisotropic droplet, our numerical simulations show an initially faster reversal of anisotropy in the BCS regime, later suppressed by the BEC fluid.Comment: 13 pages, 3 figures, presented to the 15th International Laser Physics Workshop (Lausanne, July 24-28, 2006); to be published in Laser Physic