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We study dipole-mode and scissors-mode oscillations of a harmonically-trapped dipolar supersolid, composed of dipolar droplets arranged on a one-dimensional (1D) or a two-dimensional (2D) lattice, to establish the robustness of its crystalline structure under translation and rotation, using a beyond-mean-field model including a Lee-Huang-Yang interaction. The dipolar atoms are polarized along the $z$ direction with the supersolid crystalline structure lying in the $x$-$y$ plane. A stable dipole-mode oscillation was possible in case of both quasi-1D and quasi-2D dipolar supersolids, whereas a sustained angular scissors-mode oscillation was possible only in the case of a quasi-1D dipolar supersolid between a maximum and a minimum of trap anisotropy in the $x$-$y$ plane. In both cases there was no visible deformation of the crystalline structure of the dipolar supersolid during the oscillation. The theoretical estimate of the scissors-mode-oscillation frequency was in good agreement with the present results and the agreement improved with an increase of the number of droplets in the supersolid and also with an increase in the confining trap frequencies. The results of this study can be tested experimentally with present knowhow.

Background The global health community has emphasized the importance of reporting epidemiological data by age and sex groups in the COVID-19 pandemic. However, age and sex disaggregated data of COVID-19 cases and deaths are rarely reported. Such data are very crucial for public to make truly informed choices about their own diseases risk and also for governments for public policy response. Objective To assess age and gender difference among COVID-19 cases and deaths in Nepal. Method This is a retrospective study which uses public data on COVID-19 cases and deaths released by Ministry of Health and Population, Government of Nepal from January to November, 2020. The data analysis was carried out using SPPS software version 26. Result Nepal reported 233,452 confirmed cases and 1,566 deaths of COVID-19 from 23 January 2020 to 30 November 2020. We found statistically significant differences on COVID-19 cases by age and gender in Nepal with higher number of cases among males of economically active age groups (20-60 years). Similarly, we found significant difference in COVID-19 mortality with more death occurred among male group compared to female group and with highest number of deaths among the people of above 60 years. Furthermore, we found differences in cases and deaths among provinces. Conclusion The age and gender differences in COVID cases and deaths in Nepal indicates needs of considering age and sex groups seriously while planning for testing, case management and vaccination against COVID-19 infections in Nepal.

We suggest a time-dependent mean-field hydrodynamic model for a binary dipolar boson-fermion mixture to study the stability and collapse of fermions in the $^{164}$Dy-$^{161}$Dy mixture. The condition of stability of the dipolar mixture is illustrated in terms of phase diagrams. A collapse is induced in a disk-shaped stable binary mixture by jumping the interspecies contact interaction from repulsive to attractive by the Feshbach resonance technique. The subsequent dynamics is studied by solving the time-dependent mean-field model including three-body loss due to molecule formation in boson-fermion and boson-boson channels. Collapse and fragmentation in the fermions after subsequent explosions are illustrated. The anisotropic dipolar interaction leads to anisotropic fermionic density distribution during collapse. The present study is carried out in three-dimensional space using realistic values of dipolar and contact interactions.

We suggest and study the stable disk- and cigar-shaped gap solitons of a dipolar Bose-Einstein condensate of $^{52}$Cr atoms localized in the lowest band gap by three optical-lattice (OL) potentials along orthogonal directions. The one-dimensional version of these solitons of experimental interest confined by an OL along the dipole moment direction and harmonic traps in transverse directions is also considered. Important dynamics of (i) breathing oscillation of a gap soliton upon perturbation and (ii) dragging of a gap soliton by a moving lattice along axial $z$ direction demonstrates the stability of gap solitons. A movie clip of dragging of three-dimensional gap soliton is included., Comment: To see the dragging movie clip please download source

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation using the split-step Fourier spectral method we study different aspects of the localization of a cigar-shaped interacting binary (two-component) Bose-Einstein condensate (BEC) in a one-dimensional bi-chromatic quasi-periodic optical-lattice potential, as used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)]. We consider two types of localized states: (i) when both localized components have a maximum of density at the origin x=0, and (ii) when the first component has a maximum of density and the second a minimum of density at x=0. In the non-interacting case the density profiles are symmetric around x=0. We numerically study the breakdown of this symmetry due to inter-species and intra-species interaction acting on the two components. Where possible, we have compared the numerical results with a time-dependent variational analysis. We also demonstrate the stability of the localized symmetry-broken BEC states under small perturbation., Comment: 9 pages

We derive a generalized Gross-Pitaevskii density-functional equation appropriate to study the Bose-Einstein condensate (BEC) of dimers formed of singlet spin-half Fermi pairs in the BEC-unitarity crossover while the dimer-dimer scattering length $a$ changes from 0 to $\infty$. Using an effective one-dimensional form of this equation, we study the phenomenon of dynamical self-trapping of a cigar-shaped Fermi super-fluid in the entire BEC-unitarity crossover in a double-well potential. A simple two-mode model is constructed to provide analytical insights. We also discuss the consequence of our study on the self-trapping of an atomic BEC in a double-well potential., Comment: 10 pages, 9 figures

We introduce a quasi-analytic nonlinear Schr��dinger equation with beyond mean-field corrections to describe the dynamics of a zero-temperature dilute superfluid Fermi gas in the crossover from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime, where $k_F|a| \ll 1$ with $a$ the s-wave scattering length and $k_F$ the Fermi momentum, through the unitarity limit, $k_Fa \to \pm \infty$, to the Bose regime where $k_Fa >0$. The energy of our model is parametrized using the known asymptotic behavior in the BCS, Bose, and the unitarity limits and is in excellent agreement with accurate Green function Monte Carlo calculations. The model generates good results for frequencies of collective breathing oscillation of a trapped Fermi superfluid., 4 pages, 5 figures