Scissors modes in generalized Gross–Pitaevskii equations

We investigate scissors modes in nonlinear systems with arbitrary power-law dependence of the nonlinear term. Through analytical derivation, we establish a general expression demonstrating that, in the Thomas–Fermi regime, the frequency of the scissors mode is independent of the specific form of the nonlinearity. We conclude that the scissors mode is a shear mode that does not probe the compressibility of the system, which depends on nonlinearity. To validate our findings, we perform numerical simulations of experimentally relevant Lee–Huang–Yang systems. Our results illustrate the transition of the scissors mode frequency from the non-interacting to the strongly interacting (Thomas–Fermi) regime. Finally, we demonstrate that the scissors mode frequency remains clearly identifiable even under strong quenches, which should facilitate the experimental observation of our findings.