Breathing Mode for Systems of Interacting Particles

We study the breathing mode in systems of trapped interacting particles. Our approach, based on a dynamical ansatz in the first equation of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy allows us to tackle at once a wide range of power-law interactions and interaction strengths, at linear and nonlinear levels. This both puts in a common framework various results scattered in the literature, and by widely generalizing these, emphasizes universal characters of this breathing mode. Our findings are supported by direct numerical simulations.

Figure 1

Diagram of the different regimes for the breathing mode. On the horizontal axis, the interaction range, measured by $k/d$. The interaction strength is changing along the vertical axis. Pictures of some physical examples are inserted for illustration.

Figure 2

Frequency of the linearized breathing mode as a function of the interaction strength $p$, for different values of interaction range $k$.

Figure 3

Evolution of the typical size of the cloud. The space dimension is $d=2$, and the interactions are repulsive. The parameters are $k=4$ (short-range interaction), ${\omega }_0/\kappa =17.8$ and $p=0.63$.

Figure 4

Evolution of the typical size of the cloud in one of the few negative cases. The space dimension is $d=3$, and the interactions are attractive. The parameters are $k=0$ (long-range interaction), ${\omega }_0=17.8$, $\kappa =0$ (microcanonical ensemble), and $p=2.2$. Inset: Same parameters, except $p=70$.