Chaotic Orbits in Thermal-Equilibrium Beams: Existence and Dynamical Implications

Phase mixing of chaotic orbits exponentially distributes these orbits through their accessible phase space. This phenomenon, commonly called ``chaotic mixing'', stands in marked contrast to phase mixing of regular orbits which proceeds as a power law in time. It is operationally irreversible; hence, its associated e-folding time scale sets a condition on any process envisioned for emittance compensation. A key question is whether beams can support chaotic orbits, and if so, under what conditions? We numerically investigate the parameter space of three-dimensional thermal-equilibrium beams with space charge, confined by linear external focusing forces, to determine whether the associated potentials support chaotic orbits. We find that a large subset of the parameter space does support chaos and, in turn, chaotic mixing. Details and implications are enumerated.Comment: 39 pages, including 14 figure

Prospects for thermalization of microwave-shielded ultracold molecules

We study anisotropic thermalization in dilute gases of microwave shielded polar molecular fermions. For collision energies above the threshold regime, we find that thermalization is suppressed due to a strong preference for forward scattering and a reduction in total cross section with energy, significantly reducing the efficiency of evaporative cooling. We perform close-coupling calculations on the effective potential energy surface derived by Deng et al. [Phys. Rev. Lett. 130, 183001 (2023)], to obtain accurate 2-body elastic differential cross sections across a range of collision energies. We use Gaussian process regression to obtain a global representation of the differential cross section, over a wide range of collision angles and energies. The route to equilibrium is then analyzed with cross-dimensional rethermalization experiments, quantified by a measure of collisional efficiency toward achieving thermalization.Comment: 12 pages, 4 figure

Anisotropic acoustics in dipolar Fermi gases

We consider plane wave modes in ultracold, but not quantum degenerate, dipolar Fermi gases in the hydrodynamic limit. Longitudinal waves present anisotropies in both the speed of sound and their damping, and experience a small, undulatory effect in their flow velocity. Two distinct types of shear waves appear, a ``familiar" one, and another that is accompanied by nontrivial density and temperature modulations. We propose these shear modes as an experimental means to measure the viscosity coefficients, including their anisotropies.Comment: 9 pages 3 figure

Viscous damping in weltering motion of trapped hydrodynamic dipolar Fermi gases

We consider collective motion and damping of dipolar Fermi gases in the hydrodynamic regime. We investigate the trajectories of collective oscillations -- here dubbed ``weltering'' motions -- in cross-dimensional rethermalization experiments via Monte Carlo simulations, where we find stark differences from the dilute regime. These observations are interpreted within a semi-empirical theory of viscous hydrodynamics for gases confined to anisotropic harmonic potentials. The derived equations of motion provide a simple effective theory that show favorable agreement with full numerical solutions. To do so, the theory must carefully account for the size and shape of the effective volume within which the gas' behavior is hydrodynamic. Although formulated for dipolar molecules, our theoretical framework retains a flexibility to accommodate arbitrary elastic cross sections.Comment: 13 pages, 9 figure

Total angular momentum representation for atom-molecule collisions in electric fields

It is shown that the atom-molecule collision problem in the presence of an external electric field can be solved using the total angular momentum representation in the body-fixed coordinated frame, leading to a computationally efficient method for ab initio modeling of low-temperature scattering phenomena. Our calculations demonstrate rapid convergence of the cross sections for vibrational and Stark relaxation in He-CaD collisions with the number of total angular momentum states in the basis set, leading to a 5-100 fold increase in computational efficiency over the previously used methods based on the fully uncoupled space-fixed representation. These results open up the possibility of carrying out numerically converged quantum scattering calculations on a wide array of atom-molecule collisions and chemical reactions in the presence of electric fields.Comment: 19 pages, 3 figures, 1 tabl

Fluctuations Do Matter: Large Noise-Enhanced Halos in Charged-Particle Beams

The formation of beam halos has customarily been described in terms of a particle-core model in which the space-charge field of the oscillating core drives particles to large amplitudes. This model involves parametric resonance and predicts a hard upper bound to the orbital amplitude of the halo particles. We show that the presence of colored noise due to space-charge fluctuations and/or machine imperfections can eject particles to much larger amplitudes than would be inferred from parametric resonance alone.Comment: 13 pages total, including 5 figure

Structure, Scaling and Phase Transition in the Optimal Transport Network

We minimize the dissipation rate of an electrical network under a global constraint on the sum of powers of the conductances. We construct the explicit scaling relation between currents and conductances, and show equivalence to a a previous model [J. R. Banavar {\it et al} Phys. Rev. Lett. {\bf 84}, 004745 (2000)] optimizing a power-law cost function in an abstract network. We show the currents derive from a potential, and the scaling of the conductances depends only locally on the currents. A numerical study reveals that the transition in the topology of the optimal network corresponds to a discontinuity in the slope of the power dissipation.Comment: 4 pages, 3 figure