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By developing the mean-field theory valid for large $N$, we investigate the problem of two light fermions interacting via a zero-range potential with $N$ heavy fermions in two dimensions. We obtain numerical evidence that this system is never fully bound. It always splits into droplets containing a single light atom. This is in contrast to the one-dimensional case where any number of heavy and light fermions can be bound together., Comment: 11 pages, 1 figure

The discovery of ultracold dilute liquids has significantly elevated our interest in various phenomena which go under the name of beyond-mean-field (BMF) physics. In these lecture notes we give an elementary introduction to the quantum stabilization and liquefaction of a collapsing weakly interacting Bose-Bose mixture. A detailed derivation of the leading BMF correction, also known as the Lee-Huang-Yang (LHY) term, in this system is presented in a manner suitable for further generalizations and extensions. Although the LHY term is a nonanalytic function of the density $n$, under certain conditions the leading BMF correction becomes analytic and can be expanded in integer powers of $n$, effectively introducing three-body and higher-order interactions. We discuss why and how well the Bogoliubov approach can predict these few-body observables., Comment: 36 pages, Proceedings of the International School of Physics "Enrico Fermi", Course 211 - Quantum Mixtures with Ultra-cold Atoms, July 2022

We investigate the ground state properties of $N$ bosons with attractive zero-range interactions characterized by the scattering length $a>0$ and confined to the surface of a sphere of radius $R$. We present the analytic solution of the problem for $N=2$, mean-field analysis for $N\rightarrow \infty$, and exact diffusion Monte-Carlo results for intermediate $N$. For finite $N$, we observe a smooth crossover from the uniform state in the limit $a/R\gg 1$ (weak attraction) to a localized state at small $a/R$ (strong attraction). With increasing $N$ this crossover narrows down to a discontinuous transition from the uniform state to a soliton of size $\sim R/\sqrt{N}$. The two states are separated by an energy barrier, tunneling under which is exponentially suppressed at large $N$. The system behavior is marked by a peculiar competition between space-curvature effects and beyond-mean-field terms, both breaking the scaling invariance of a two-dimensional mean-field theory., Comment: 10 pages, 3 figures

We study binding of $N$ identical heavy fermions by a light atom in two dimensions assuming zero-range attractive heavy-light interactions. By using the mean-field theory valid for large $N$ we show that the $N+1$ cluster is bound when the mass ratio exceeds $1.074N^2$. The mean-field theory, being scale invariant in two dimensions, predicts only the shapes of the clusters leaving their sizes and energies undefined. By taking into account beyond-mean-field effects we find closed-form expressions for these quantities. We also discuss differences between the Thomas-Fermi and Hartree-Fock approaches for treating the heavy fermions., Comment: 11 pages, 3 figures

For sufficiently large mass ratios the attractive exchange force caused by a single light atom interacting with a few heavy identical fermions can overcome their Fermi degeneracy pressure and bind them into an $N+1$ cluster. Here, by using a mean-field approach valid for large $N$, we find that $N+1$ clusters can attract each other and form a self-bound charge density wave, the properties of which we fully characterize. Our work shows that there are no fundamental obstacles for having self-bound states in fermionic mixtures with zero-range interactions., Comment: 11 pages, 4 figures

We present results of polarimetric, photometric, and spectral observations of the near-Earth asteroid (3200) Phaethon carried out at the 6-m BTA telescope of the Special Astrophysical Observatory and the 2.6-m and 1.25-m telescopes of the Crimean Astrophysical Observatory over a wide range of phase angles during its close approach to the Earth at the end of 2017 (19-135 deg) and in 2020 at \alpha = 52.2 deg. Using our and other available in literature data, we found that the maximum degree of linear polarization of Phaethon in the V band is 45% at the phase angle 124 deg. Using the dependence (polarimetric slope-albedo) we have found the geometric albedo of asteroid Phaethon to be 0.06. This value falls into the lower range of albedo values for asteroids determined by different methods. The mean color indices U-B=0.207 and B-V=0.639 of the asteroid are derived at heliocentric and geocentric distances 1.077 au and 0.102 au, respectively. The effective diameter of Phaethon is estimated from obtained absolute magnitude and geometrical albedo, it is equal to 6.8 km. The best fit to the observed polarimetric data was obtained with the Sh-matrix model of conjugated random Gaussian particles composed of Mg-rich silicate (90%) and amorphous carbon (10%)., Comment: 27 pages, 9 figures

We consider the problem of $N$ identical fermions interacting via a zero-range attractive potential with a lighter atom in one dimension. Using the few-body approach based on the Skorniakov and Ter-Martirosian equation, we determine the energies and the critical mass ratios for the emergence of the tetramer, pentamer, and hexamer. For large $N$, we solve the problem analytically by using the mean-field theory based on the Thomas-Fermi approximation. The system becomes bound when the heavy-to-light mass ratio exceeds a critical value which grows as $N^3$ at large $N$. We also employ a more sophisticated Hartree-Fock approach, which turns out to be equivalent to the Thomas-Fermi approximation for determining the energies, but provides a better description of the microscopic structure of the clusters., Comment: 6 pages, 2 figures

We theoretically calculate and experimentally measure the beyond-mean-field (BMF) equation of state in a coherently-coupled two-component Bose-Einstein condensate (BEC) in the regime where averaging of the interspecies and intraspecies coupling constants over the hyperfine composition of the single-particle dressed state predicts the exact cancellation of the two-body interaction. We show that with increasing the Rabi-coupling frequency $\Omega$, the BMF energy density crosses over from the nonanalytic Lee-Huang-Yang (LHY) scaling $\propto n^{5/2}$ to an expansion in integer powers of density, where, in addition to a two-body BMF term $\propto n^2 \sqrt{\Omega}$, there emerges a repulsive three-body contribution $\propto n^3/\sqrt{\Omega}$. We experimentally evidence this two contributions, thanks to their different scaling with $\Omega$, in the expansion of a Rabi-coupled two-component $^{39}$K condensate in a waveguide. By studying the expansion with and without Rabi coupling, we reveal an important feature relevant for observing BMF effects and associated phenomena in mixtures with spin-asymmetric losses: Rabi coupling helps preserve the spin composition and thus prevents the system from drifting away from the point of vanishing mean field.

We develop the perturbation theory for bosons interacting via a two-body potential $V$ of vanishing mean value. We find that the leading nonpairwise contribution to the energy emerges in the third order in $V$ and represents an effective three-body interaction, the sign of which in most cases (although not in general) is anticorrelated with the sign of the long-range tail of $V$. Explicit results are obtained for a few particular two-body interaction potentials and we perform a detailed perturbative analysis of tilted dipoles in quasi-low-dimensional geometries., Comment: 11 pages, 1 figure

Repulsive Bose-Bose mixtures are known to either mix or phase-separate into pure components. Here we predict a mixed-bubble regime in which bubbles of the mixed phase coexist with a pure phase of one of the components. This is a beyond-mean-field effect which occurs for unequal masses or unequal intraspecies coupling constants and is due to a competition between the mean-field term, quadratic in densities, and a nonquadratic beyond-mean-field correction. We find parameters of the mixed-bubble regime in all dimensions and discuss implications for current experiments., Comment: 2 figures; 9 pages

We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a two-dimensional mixture of A and B bosons, with attractive AB and equally repulsive AA and BB interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attraction-to-repulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced AABB and AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced ABB trimer, ABBB tetramer, and AABBB pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2 a_{BB}$ where the atom-dimer interaction switches to repulsion., Comment: 3 figures

Fundamental parameters are determined for three bright, nearby K-giants, {\beta} Gem (K0 III), {\mu} Leo (K2 III), and {\alpha} Tau (K5 III). It is notable that around all three stars the giant planets have been found. Our results are compared with published high-precision data for benchmark stars included in the Gaia project. Very good agreement was obtained for all three giants with these data for the basic parameters Teff, logg, and M. Special attention was devoted to analysis of the Fe I lines which are the basis of a simultaneous determination of the metallicity index [Fe/H] and microturbulent parameter Vt. The equivalent widths W of the Fe I lines are automatically measured from published spectra for the benchmark stars. An analysis of Fe I lines from the list of "golden lines" selected in a study of benchmark stars led to the conclusion that the excitation potential El of the low level of the lines plays an substantial role in determining [Fe/H] and Vt. It is shown that in the case of the early K-giants {\beta} Gem and {\mu} Leo for lines in the range of W from 100 to 300 m{\AA} there is a dependence of the [Fe/H] and Vt values on El. It is shown that a correct accounting for it leads an ambiguity in the determination of [Fe/H] and Vt for {\beta} Gem and {\mu} Leo. In the case of the coolest K-giant {\alpha} Tau (Aldebaran) with a temperature Teff = 3920K, this effect seems to be less pronounced. Recommendations are given for the Fe I lines selection for [Fe/H] and Vt determination. It is sonfirmed for the example of the three stars studied here that the non-LTE effects in the Fe I lines for the K-giants with normal metallicity are very minor, so they cannot be the reason of the revealed ambiguity in [Fe/H] and Vt values. The low ratios of the carbon 12C/13C and oxygen 16O/17O isotopes confirm that all three giants passed the phase of deep convective mixing., Comment: 22 pages, 6 figures, 6 tables

We calculate the effective three-body force for bosons interacting with each other by a two-body potential tuned to a narrow zero crossing in any dimension. We use the standard two-channel model parametrized by the background atom-atom interaction strength, the amplitude of the open-channel to closed-channel coupling, and the atom-dimer interaction strength. The three-body force originates from the atom-dimer interaction, but it can be dramatically enhanced for narrow crossings, i.e., for small atom-dimer conversion amplitudes. This effect can be used to stabilize quasi-two-dimensional dipolar atoms and molecules., Comment: published version

We solve the three-boson problem with contact two- and three-body interactions in one dimension and analytically calculate the ground and excited trimer-state energies. Then, by using the diffusion Monte Carlo technique we calculate the binding energy of three dimers formed in a one-dimensional Bose-Bose or Fermi-Bose mixture with attractive interspecies and repulsive intraspecies interactions. Combining these results with our three-body analytics we extract the three-dimer scattering length close to the dimer-dimer zero crossing. In both considered cases the three-dimer interaction turns out to be repulsive. Our results constitute a concrete proposal for obtaining a one-dimensional gas with a pure three-body repulsion., Comment: published version

We consider the system of dimers formed in a one-dimensional mass-balanced Bose-Bose mixture of species $\sigma=\uparrow$, $\downarrow$ with attractive interspecies and repulsive intraspecies contact interactions. In the plane parametrized by the ratios of the coupling constants $g_{\uparrow\uparrow}/|g_{\uparrow\downarrow}|$ and $g_{\downarrow\downarrow}/|g_{\uparrow\downarrow}|$ we trace out the curve where the dimer-dimer interaction switches from attractive to repulsive. We find this curve to be significantly (by more than a factor of 2) shifted towards larger $g_{\sigma\sigma}$ (or smaller $|g_{\uparrow\downarrow}|$) compared to the mean-field stability boundary $g_{\uparrow\uparrow}g_{\downarrow\downarrow}=g_{\uparrow\downarrow}^2$. For a weak dimer-dimer attraction we predict a dilute dimerized liquid phase stabilized against collapse by a repulsive three-dimer force., Comment: published version

A five-dimensional interpolation method and corresponding computer program are developed for using published calculations to determine the non-LTE correction {\Delta\}NLTE to the lithium abundance log{\epsilon}(Li) derived from the Li I 6707.8 {\AA} line. The {\Delta\}NLTE values is determined from the following five parameters: {\Delta\}NLTE the effective temperature Teff, the acceleration of gravity logg, the metallicity index [Fe/H], the microturbulent velocity Vt, and the LTE Li abundance log {\epsilon}(Li). The program is used to calculate values of {\Delta\}NLTE and the non-LTE Li abundance for 91 single bright giants from the list of Lebre, et al. By combining these results with data for 55 stars, we obtain the non-LTE values of log {\epsilon}(Li) for 146 FGK-giants and supergiants. We confirm that, in the spectra of most of these stars, it is only possible to estimate for them an upper limit for the Li abundance. A large spread is confirmed in log {\epsilon}(Li) for stars with masses M<6Msun. A comparison of these results with model calculations of stars confirms the unique sensitivity of the lithium abundance to the initial rotation velocity V0. We discuss the giants and supergiants with lithium abundances log {\epsilon}(Li) = 1.4 +- 0.3, which could have a rotation velocity V0=0 km/s and have already undergone deep convective mixing. Li-rich giants with lithium abundances log {\epsilon}(Li)>2 and nearly up to the initial value of log {\epsilon}(Li) = 3.2 +- 0.1 are examined. It is shown that the fraction of Li-rich giants with V0 = 0 - 50 km/s is consistent with current evolutionary models. The other stars of this type, as well as all of the "super Li-rich" giants, for which the standard theory is untenable, can be explained by invoking the hypothesis of recent lithium synthesis in the star or an alternative hypothesis according to which a giant planet is engulfed by the star., Comment: 15 pages, 5 figures, 2 tables

We study the two-body scattering problem in the zero-range approximation with a sinusoidally driven scattering length and calculate the relation between the mean value and amplitude of the drive for which the effective scattering amplitude is resonantly enhanced. In this manner we arrive at a family of curves along which the effective scattering length diverges but the nature of the corresponding Floquet-induced resonance changes from narrow to wide. Remarkably, on these curves the driving does not induce heating. In order to study the effect of these resonances on the three-body problem we consider one light and two heavy particles with driven heavy-light interaction in the Born-Oppenheimer approximation and find that the Floquet driving can be used to tune the three-body and inelasticity parameters., Comment: 14 pages, 7 figures