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It has been shown [H. Chaté et al., Phys. Rev. E 77, 046113 (2008) and F. Ginelli, Eur. Phys. J.: Spec. Top. 225, 2099 (2016)] that the hydrodynamic equations of dry active polar fluids (i.e., moving flocks without momentum conservation) imply giant number fluctuations. Specifically, the rms fluctuations ⟨ (δ N) 2 ⟩ of the number N of active particles in a region containing a mean number of active particles ⟨N⟩ scale according to the law ⟨ (δ N) 2 ⟩ = K ′ ⟨ N ⟩ ϕ (d) with ϕ (d) = 7 10 + 1 5 d in d ≤ 4 spatial dimensions. This is much larger than the "law of large numbers" scaling ⟨ (δ N) 2 ⟩ = K ⟨ N ⟩ found in most equilibrium and nonequilibrium systems. In this paper, it is demonstrated that giant number fluctuations also depend singularly on the shape of the box in which one counts the particles, vanishing in the limit of very thin and very fat boxes. These fluctuations arise not from large density fluctuations—indeed, the density fluctuations in polar ordered dry active fluids are not in general particularly large—but from long ranged spatial correlations between those fluctuations. These are shown to be closely related in two spatial dimensions to the electrostatic potential near a sharp upward pointing conducting wedge of opening angle 3 π 4 = 135 ° and in three dimensions to the electrostatic potential near a sharp upward pointing charged cone of opening angle 37.16°. This very precise prediction can be stringently tested by alternative box counting experiments that directly measure the direction dependence, as well as the scaling with distance, of the density-density correlation function. [ABSTRACT FROM AUTHOR]

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [NL-eEDM Collaboration, Eur. Phys. J. D 72, 197 (2018)]. Knowledge of the molecular properties of BaF is thus needed to plan the measurements and, in particular, to determine the optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require the incorporation of both high-order correlation and relativistic effects in the calculations. In this work, theoretical investigations of the ground and lowest excited states of BaF and its lighter homologs, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster and multireference configuration interaction methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the A 2 Π 1 / 2 → X 2 Σ 1 / 2 + transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the B 2 Σ 1 / 2 + → X 2 Σ 1 / 2 + transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the nondiagonal nature of the FCFs in this system. Special attention is given to the properties of the A′2Δ state, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and excited states of the three molecules and the transition dipole moments (TDMs) between the different states. Finally, using the calculated FCFs and TDMs, we determine that the A 2 Π 1 / 2 → X 2 Σ 1 / 2 + transition is suitable for transverse cooling in BaF. [ABSTRACT FROM AUTHOR]

In the case of an adiabatic motion in molecules, electrons adjust to the smoothly changing geometry of the nuclei. Although then the Born-Oppenheimer (BO) approximation is valid, it fails in predicting the time-dependence of electron momenta because, within its product ansatz for the wave function, the respective expectation values are zero. It is shown that this failure can be circumvented using the Ehrenfest theorem. Here we extend our former work [T. Schaupp et al., Eur. Phys. J. B 91, 97 (2018)] and regard models in higher dimensions and for more particles. We solve the time-dependent Schrödinger equation for the combined nuclear-electronic motion and compare the results to those derived from BO wave functions. For all situations, it is found that the time-dependent BO electronic momenta are in excellent agreement with the numerically exact results. [ABSTRACT FROM AUTHOR]