Density response of a trapped Fermi gas: a crossover from the pair vibration mode to the Goldstone mode

We consider the density response of a trapped two-component Fermi gas. Combining the Bogoliubov-deGennes method with the random phase approximation allows the study of both collective and single particle excitations. Calculating the density response across a wide range of interactions, we observe a crossover from a weakly interacting pair vibration mode to a strongly interacting Goldstone mode. The crossover is associated with a depressed collective mode frequency and an increased damping rate, in agreement with density response experiments performed in strongly interacting atomic gases.Comment: 14 pages, 8 figure

Study of distortion effects and clustering of isotopic impurities in solid molecular para-hydrogen by Shadow Wave Functions

We employed a fully optimized Shadow Wave Function (SWF) in combination with Variational Monte Carlo techniques to investigate the properties of HD molecules and molecular ortho-deuterium (o-D_2) in bulk solid para-hydrogen (p-H_2). Calculations were performed for different concentrations of impurities ranging from about 1% to 25% at the equilibrium density for the para-hydrogen crystal. By computing the excess energy both for clustered and isolated impurities we tried to determine a limit for the solubility of HD and o-D_2 in p-H_2.Comment: 4 pages, 4 figure

Probing the FFLO phase by double occupancy modulation spectroscopy

We propose here that for a spin-imbalanced two-component attractive Fermi gas loaded in a 1D optical lattice in presence of an harmonic confining potential, the observation of the change in the double occupancy after a lattice depth modulation can provide clear evidence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Simulating the time evolution of the system, we can characterize the double occupancy spectrum for different initial conditions, relating its features to the FFLO wavevector $q$. In particular, the narrowing of the width of the spectrum can be related, through Bethe-ansatz equations in the strongly interacting limit, to the FFLO wavevector $q$.Comment: 4 pages, 6 figure

Diffusion Approximation with Equilibrium for Evolutionary Systems Switched by Semi-Markov Processes

We consider an evolutionary system switched by a semi-Markov process. For this system, we obtain an inhomogeneous diffusion approximation results where the initial process is compensated by the averaging function in the average approximation scheme.Для систем, що перемикаються иапівмарковськими процесами, одержано результати про неоднорідну дифузійну апроксимацію, де вихідний процес компенсується усередненою функцією в апроксимаційній схемі усереднення

Systematization and classification of risks in the economic sciences

Досліджено існуючі підходи до класифікації ризиків та систематизовано їх залежно від галузі економічної науки. На основі огляду наукових праць вітчизняних та зарубіжних вчених систематизовано та прокласифіковано ризики за такими галуззями економічної науки: політична економія, фінанси (страхування), облік, математична економіка, менеджмент, аналіз, економіка підприємства. Дослідження наукових праць дозволило встановити ряд науковців, які вивчали класифікацію ризиків у цілому в економіці без виділення конкретних галузей економіки. Визначено структуру класифікації ризиків та систематизовано багаторівневі класифікації ризиків. Обгрунтовано використання дво- трирівневих класифікаторів, що полегшує вимірювання й оцінювання ризиків та є придатними для практичного використання.The existing approaches to risk classification are investigated and systematized in the article, depending on the branch of economics. Based on the review of scientific works of national and foreign scientists the risks are systematized and classified according to the following branches of economics: political economy, finance (insurance), accounting, mathematical economics, management, analysis, business economics. Taking into account limitations in volume of article and a sufficiently large of number of scientific papers on risk classification, the approaches to risk classification of individual members of different branches of economics are disclosed in the article. The research of scientific papers allows to establish a number of scientists who have studied the classification of risks in the economy as a whole without providing specific industries. The structure of risk classification is determined and multi-risk classification are systematized in the article. Using the two or three-level classifiers proved by the author that facilitates the measurement and assessment of risk and is appropriate for a practical use. It is detected that some scientists in their research as prospects for further research in this area offer to build a matrixes and typical risk profile (risk maps, risk passports), justifying it as a necessary condition and effectively manage risks. As a whole overview of sources on risk classification makes it possible to confirm that different groups of scientists investigate the classification of risks from the perspective of their professional activities

Основні підходи до визначення поняття “ризик”

Вивчено та узагальнено підходи до визначення поняття “ризик” у сучасній вітчизняній та зарубіжній літературіThe approaches to the definition of “risk” in modern domestic and foreign literature are researched and generalize