Regime variance testing - a quantile approach

This paper is devoted to testing time series that exhibit behavior related to two or more regimes with different statistical properties. Motivation of our study are two real data sets from plasma physics with observable two-regimes structure. In this paper we develop estimation procedure for critical point of division the structure change of a time series. Moreover we propose three tests for recognition such specific behavior. The presented methodology is based on the empirical second moment and its main advantage is lack of the distribution assumption. Moreover, the examined statistical properties we express in the language of empirical quantiles of the squared data therefore the methodology is an extension of the approach known from the literature. The theoretical results we confirm by simulations and analysis of real data of turbulent laboratory plasma

Pairing in a system of a few attractive fermions in a harmonic trap

We study a strongly attractive system of a few spin-1/2 fermions confined in a one-dimensional harmonic trap, interacting via two-body contact potential. Performing exact diagonalization of the Hamiltonian we analyze the ground state and the thermal state of the system in terms of one-- and two--particle reduced density matrices. We show how for strong attraction the correlated pairs emerge in the system. We find that the fraction of correlated pairs depends on temperature and we show that this dependence has universal properties analogous to the gap function known from the theory of superconductivity. In contrast to the standard approach based on the variational ansatz and/or perturbation theory, our predictions are exact and are valid also in a strong attraction limit. Our findings contribute to the understanding of strongly correlated few-body systems and can be verified in current experiments on ultra-cold atoms.Comment: 6 figure

The orbital structure of a tidally induced bar

Orbits are the key building blocks of any density distribution and their study helps us understand the kinematical structure and the evolution of galaxies. Here we investigate orbits in a tidally induced bar of a dwarf galaxy, using an $N$-body simulation of an initially disky dwarf galaxy orbiting a Milky Way-like host. After the first pericenter passage, a tidally induced bar forms in the stellar component of the dwarf. The bar evolution is different than in isolated galaxies and our analysis focuses on the period before it buckles. We study the orbits in terms of their dominant frequencies, which we calculate in a Cartesian coordinate frame rotating with the bar. Apart from the well-known x$_1$ orbits we find many other types, mostly with boxy shapes of various degree of elongation. Some of them are also near-periodic, admitting frequency ratios of 4/3, 3/2 and 5/3. The box orbits have various degrees of vertical thickness but only a relatively small fraction of those have banana (i.e. smile/frown) or infinity-symbol shapes in the edge-on view. In the very center we also find orbits known from the potential of triaxial ellipsoids. The elongation of the orbits grows with distance from the center of the bar in agreement with the variation of the shape of the density distribution. Our classification of orbits leads to the conclusion that more than $80 \%$ of them have boxy shapes, while only $8 \%$ have shapes of classical x$_1$ orbits.Comment: 15 pages, 15 figures, accepted for publication in Ap

Tidally induced bars in dwarf galaxies on different orbits around a Milky Way-like host

Bars in galaxies may develop through a global instability or due to an interaction with another system. We study bar formation in disky dwarf galaxies orbiting a Milky Way-like galaxy. We employ $N$-body simulations to study the impact of initial orbital parameters: the size of the dwarf galaxy orbit and the inclination of its disc with respect to the orbital plane. In all cases a bar develops in the center of the dwarf during the first pericenter on its orbit around the host. Between subsequent pericenter passages the bars are stable, but at the pericenters they are usually weakened and shortened. The initial properties and details of the further evolution of the bars depend heavily on the orbital configuration. We find that for the exactly prograde orientation, the strongest bar is formed for the intermediate-size orbit. On the tighter orbit, the disc is too disturbed and stripped to form a strong bar. On the wider orbit, the tidal interaction is too weak. The dependence on the disc inclination is such that weaker bars form in more inclined discs. The bars experience either a very weak buckling or none at all. We do not observe any secular evolution, possibly because the dwarfs are perturbed at each pericenter passage. The rotation speed of the bars can be classified as slow ($R_\mathrm{CR}/l_\mathrm{bar}\sim2-3$). We attribute this to the loss of a significant fraction of the disc's rotation during the encounter with the host galaxy.Comment: 17 pages, 14 figures, accepted to Ap

Coherence properties of spinor condensates at finite temperatures

We consider a spinor condensate of 87Rb atoms in its F=1 hyperfine state at finite temperatures. Putting initially all atoms in m_F=0 component we find that the system evolves into the state of thermal equilibrium. This state is approached in a step-like process and when established it manifests itself in distinguishable ways. The atoms in states m_F=+1 and m_F=-1 start to rotate in opposite directions breaking the chiral symmetry and showing highly regular spin textures. Also the coherence properties of the system changes dramatically. Depending on the strength of spin-changing collisions the system first enters the stage where the m_F=+1 and m_F=-1 spinor condensate components periodically loose and recover their mutual coherence whereas their thermal counterparts get completely dephased. For stronger spin changing collisions the system enters the regime where also the strong coherence between other components is built up.Comment: 5 pages, 4 figure