Bir boyutlu yumuşak çekirdekli bozon sistemlerinde kollektif uyarılar ve yoğunluk-dalga kararsızlıkları

We investigated the dynamics of bosons interacting with Rydberg-dressed potentials in single-wire and double-wire structures. Specifically, we aimed to understand how the addition of Rydberg dressing, with its soft-core nature and van der Waals tail at long distances, influences the behavior of single-wire and double wire systems of bosons. This investigation was conducted using the random phase approximation (RPA) and the Bogoliubov-de Gennes (BdG) mean-field approximation at zero temperature, focusing on the emergence of collective modes and density-wave instabilities. We examined the dispersions of collective modes in single-wire and double-wire structures of bosons with Rydberg-dressed interactions. In the long-wavelength limit, symmetric and anti-symmetric modes show linear behavior in wave vectors with distinct sound velocities. A prominent maxon-roton feature appears at intermediate wave vectors, especially at large coupling constants. The influence of wire spacing on mode dispersion is significant: smaller spacings lead to the disappearance of the asymmetric mode with free-particle-like dispersion, while larger spacings result in mode degeneracy in symmetric bi-wires due to diminished inter-wire coupling. The system becomes unstable toward density-waves at strong couplings, indicated by the vanishing roton energy, affecting both symmetric and anti-symmetric branches. Additionally, density imbalances between wires shift the energy of the excitation branches and destabilize the homogeneous superfluid phase at lower coupling constants. While the roton softening observed suggests instability toward density-modulated phases, more sophisticated numerical methods are needed to characterize these phases accurately.