Global hypoellipticity and global solvability for vector fields on compact Lie groups

We present necessary and sufficient conditions to have global hypoellipticity and global solvability for a class of vector fields defined on a product of compact Lie groups. In view of Greenfield's and Wallach's conjecture, about the non-existence of globally hypoelliptic vector fields on compact manifolds different from tori, we also investigate different notions of regularity weaker than global hypoellipticity and describe completely the global hypoellipticity and global solvability of zero-order perturbations of our vector fields. We also present a class of vector fields with variable coefficients whose operators can be reduced to a normal form, and we prove that the study of the global properties of such operators is equivalent to the study of the respective properties for their normal forms.Comment: 43 page

Magnetic and electric dipole moments of the H^3 Δ_1 state in ThO

The metastable H^3 Δ_1 state in the thorium monoxide (ThO) molecule is highly sensitive to the presence of a CP -violating permanent electric dipole moment of the electron (eEDM) [E. R. Meyer and J. L. Bohn, Phys. Rev. A 78, 010502 (2008)]. The magnetic dipole moment μ_H and the molecule-fixed electric dipole moment D_H of this state are measured in preparation for a search for the eEDM. The small magnetic moment μH=8.5(5)×10^(−3)μ_B displays the predicted cancellation of spin and orbital contributions in a ^3Δ_1 paramagnetic molecular state, providing a significant advantage for the suppression of magnetic field noise and related systematic effects in the eEDM search. In addition, the induced electric dipole moment is shown to be fully saturated in very modest electric fields (<10 V/cm). This feature is favorable for the suppression of many other potential systematic errors in the ThO eEDM search experiment

The current crisis of academia-led research: A threat to the common good? Preliminary data from Europe and the United States

Objective: This research note aimed to analyze the scientific productivity trends 2015-2019, focusing on the top 30 universities in Europe and United States and on the top 30 private companies - as classified in the SCImago Institutions Ranking. Our hypothesis is that private companies are gaining an increasingly prominent role in the research field, while academia is losing its predominance. Results: From 2015 to 2019, all universities in Europe and the United States lost positions in the scientific production ranking, while private companies gained positions. These trends seem to be driven mainly by the scientific productivity sub-indicator "Innovation". These data suggest that the role private companies will play in the future will not be limited to support research economically or influence it from "outside". Private companies have taken a path that may lead them to directly control all stages of production/communication of knowledge, including research - a role once bestowed on universities. Our data, although preliminary, seem to suggest that, at present, academia risks losing its predominance in the research field. This scenario deserves attention because of the threats it may pose to the independence of research and its role in supporting human equity and sustainable health for all

Spectrum generating algebra for the continuous spectrum of a free particle in Lobachevski space

In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical symmetry algebra of the system plus a subalgebra of operators that give the spectrum of the system and connects the eigenfunctions of the Hamiltonian among themselves. In our case, the geometrical symmetry algebra is $\frak{so}(3,1)$ and the SGA is $\frak{so}(4,2)$. We start with a representation of $\frak{so}(4,2)$ by functions on a realization of the Lobachevski space given by a two sheeted hyperboloid, where the Lie algebra commutators are the usual Poisson-Dirac brackets. Then, introduce a quantized version of the representation in which functions are replaced by operators on a Hilbert space and Poisson-Dirac brackets by commutators. Eigenfunctions of the Hamiltonian are given and "naive" ladder operators are identified. The previously defined "naive" ladder operators shift the eigenvalues by a complex number so that an alternative approach is necessary. This is obtained by a non self-adjoint function of a linear combination of the ladder operators which gives the correct relation among the eigenfunctions of the Hamiltonian. We give an eigenfunction expansion of functions over the upper sheet of two sheeted hyperboloid in terms of the eigenfunctions of the Hamiltonian.Comment: 23 page

Optically trapped Feshbach molecules of fermionic 161Dy and 40K

We report on the preparation of a pure ultracold sample of bosonic DyK Feshbach molecules, which are composed of the fermionic isotopes 161Dy and 40K. Employing a magnetic sweep across a resonance located near 7.3 G, we produce up to 5000 molecules at a temperature of about 50 nK. For purification from the remaining atoms, we apply a Stern-Gerlach technique based on magnetic levitation of the molecules in a very weak optical dipole trap. With the trapped molecules we finally reach a high phase-space density of about 0.1. We measure the magnetic field dependence of the molecular binding energy and the magnetic moment, refining our knowledge of the resonance parameters. We also demonstrate a peculiar anisotropic expansion effect observed when the molecules are released from the trap and expand freely in the magnetic levitation field. Moreover, we identify an important lifetime limitation that is imposed by the 1064-nm infrared trap light itself and not by inelastic collisions. The light-induced decay rate is found to be proportional to the trap light intensity and the closed-channel fraction of the Feshbach molecule. These observations suggest a one-photon coupling to electronically excited states to limit the lifetime and point to the prospect of loss suppression by optimizing the wavelength of the trapping light. Our results represent important insights and experimental steps on the way to achieve quantum-degenerate samples of DyK molecules and novel superfluids based on mass-imbalanced fermion mixtures

Relativistic Quantum Thermodynamics of Ideal Gases in 2 Dimensions

In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.Comment: 6 pages, 1 figur

Magnetic and electric dipole moments of the H 3Δ1H\ {}^3\Delta_1 state in ThO

The metastable $H \ {}^3\Delta_1$ state in the thorium monoxide (ThO) molecule is highly sensitive to the presence of a CP-violating permanent electric dipole moment of the electron (eEDM). The magnetic dipole moment $\mu_H$ and the molecule-fixed electric dipole moment $D_H$ of this state are measured in preparation for a search for the eEDM. The small magnetic moment $\mu_H = 8.5(5) \times 10^{-3} \ \mu_B$ displays the predicted cancellation of spin and orbital contributions in a ${}^3 \Delta_1$ paramagnetic molecular state, providing a significant advantage for the suppression of magnetic field noise and related systematic effects in the eEDM search. In addition, the induced electric dipole moment is shown to be fully saturated in very modest electric fields ($<$ 10 V/cm). This feature is favorable for the suppression of many other potential systematic errors in the ThO eEDM search experiment.Comment: 4 pages, 3 figure

R-matrix presentation for (super)-Yangians Y(g)

We give a unified RTT presentation of (super)-Yangians Y(g) for so(n), sp(2n) and osp(m|2n).Comment: 9 page