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Abstract Quasi-periodic motions can be numerically found in piecewise-linear systems, however, their characteristics have not been well understood. To illustrate this, an incremental harmonic balance (IHB) method with two timescales is extended in this work to analyze quasi-periodic motions of a non-smooth dynamic system, i.e., a gear transmission system with piecewise linearity stiffness. The gear transmission system is simplified to a four degree-of-freedom nonlinear dynamic model by using a lumped mass method. Nonlinear governing equations of the gear transmission system are formulated by utilizing the Newton’s second law. The IHB method with two timescales applicable to piecewise-linear systems is employed to examine quasi-periodic motions of the gear transmission system whose Fourier spectra display uniformly spaced sideband frequencies around carrier frequencies. The Floquet theory is extended to analyze quasi-periodic solutions of piecewise-linear systems based on introduction of a small perturbation on a steady-state quasi-periodic solution of the gear transmission system with piecewise linearities. Comparison with numerical results calculated using the fourth-order Runge-Kutta method confirms that excellent accuracy of the IHB method with two timescales can be achieved with an appropriate number of harmonic terms. 

We measure universal temperature-independent density shifts for the thermal conductivity ${\kappa }_T$and shear viscosity $\eta$, relative to the high temperature limits, for a normal phase unitary Fermi gas confined in a box potential. We show that a time-dependent kinetic theory model enables extraction of the hydrodynamic transport times ${\tau }_{\eta }$and ${\tau }_{\kappa }$from the time-dependent free decay of a spatially periodic density perturbation, yielding the static transport properties and density shifts, corrected for finite relaxation times. Published by the American Physical Society2024 

We derive a model to explain the observed suppression of optically induced loss in a weakly interacting Fermi gas as the s-wave scattering length is increased [C. A. Royse et al., Phys. Rev. Lett. 133, 083404 (2024)]. We incorporate spin-dependent loss into a quasiclassical collective spin vector model to show that loss suppression occurs via a transition to a magnetized dynamical state, where two-body s-wave scattering is inhibited via the Pauli principle. By comparing measurements in mixtures and coherently prepared samples, we show that the data are quantitatively explained by the model, which is applicable to the optical control of energy-space lattices for new quantum simulators. 

We observe strong dynamical suppression of optically induced loss in a weakly interacting Fermi gas as the s-wave scattering length is increased. A single trapped cigar-shaped cloud behaves as a large spin lattice in energy space with a tunable Heisenberg Hamiltonian. The loss suppression occurs as the lattice transitions into a magnetized state, where the fermionic nature of the atoms inhibits interactions. The data are quantitatively explained by incorporating spin-dependent loss into a quasiclassical collective spin vector model, the success of which enables the application of optical control of effective long-range interactions to this system.