Super Tonks-Girardeau state in an attractive one-dimensional dipolar gas

The ground state of a one-dimensional (1D) quantum gas of dipoles oriented perpendicular to the longitudinal axis, with a strong 1/x^3 repulsive potential, is studied at low 1D densities $n$. Near contact the dependence of the many-body wave function on the separation x_{jl} of two particles reduces to a two-body wave function \Psi_{rel}(x_{jl}). Immediately after a sudden rotation of the dipoles so that they are parallel to the longitudinal axis, this wave function will still be that of the repulsive potential, but since the potential is now that of the attractive potential, it will not be stationary. It is shown that as nd^2 -> 0 the rate of change of this wave function approaches zero. It follows that for small values of nd^2, this state is metastable and is an analog of the super Tonks-Girardeau state of bosons with a strong zero-range attraction. The dipolar system is equivalent to a spinor Fermi gas with spin $z$ components \sigma_{\uparrow}=\perp (perpendicular to the longitudinal axis) and \sigma_{\downarrow}=|| (parallel to the longitudinal axis). A Fermi-Fermi mapping from spinor to spinless Fermi gas followed by the standard 1960 Fermi-Bose mapping reduces the Fermi system to a Bose gas. Potential experiments realizing the sudden spin rotation with ultracold dipolar gases are discussed, and a few salient properties of these states are accurately evaluated by a Monte Carlo method.Comment: 5 pages, 2 figures, revtex4. Published versio

Modules over the small quantum group and semi-infinite flag manifold

We develop a theory of perverse sheaves on the semi-infinite flag manifold $G((t))/N((t))\cdot T[[t]]$, and show that the subcategory of Iwahori-monodromy perverse sheaves is equivalent to the regular block of the category of representations of the small quantum group at an even root of unity

Fifty years of the Glauber diffraction theory

In this minireview a historical excursus in theoretical studies related to the Glauber diffraction theory has been presented with an accent on the recent developments in this subject.Comment: 22 pages, 4 figures, in russian;v2: an atempt to improve hyphenatio

Gravitational sedimentation of cloud of solid spherical particles at small Reynolds numbers

The experimental results of study of gravitational sedimentation of highly-concentrated systems of solid spherical particles at small Reynolds numbers Re<1 are presented. Empirical equation for drag coefficient of the particle assembly has been obtained. The influence of initial particle concentration in the cloud on its dynamics and velocity has been analysed

Identification of size and concentration of submicron particles on the basis of rayleigh scattering model

A method of identification of maximum size and concentration of submicron aerosol particles based on measurement of intensity attenuation of a parallel beam of probe optical radiation is described. Offered method makes it possible to determine both particle concentration and maximum particle size with controlled accuracy for aerosol media without any initial information about particle size distribution

Dynamics of bubble rising at small Reynolds numbers

Results of experimental study of a single spherical bubble rising in the non-stationary regime in a viscous liquid (with and without surfactant) at small Reynolds numbers Re<1 have been presented. Improved empirical correlations for drag coefficient of the bubble rising with and without surfactant in the stationary regime have been obtained. Influence of nonstationary effects on the dynamics of bubble rising has been analyzed

Estimation of the activity of lead in the binary Pb-Sb and Pb-Bi systems

The activity of lead in its alloys with bismuth and antimony is estimated by the least squares method and interval analysis. The interval method of processing the experimental results is shown to calculate the reliable ranges of the estimated parameters in the dependences of thermodynamic functions and the actual level of the total measurement errors. © 2013 Pleiades Publishing, Ltd

Unsteady rise of a bubble in a viscous fluid at small Reynolds numbers

A bubble rising from the state of rest in a viscous incompressible fluid is considered. A formula for the Basset force acting on the bubble in a viscous fluid is obtained, which differs by a multiplier from the Basset force for a solid particle. The problem of unsteady rise of a bubble is solved analytically. The bubble rise is also studied experimentally and the experimental data are compared with the theoretical results