Dark soliton past a finite size obstacle: adiabatic approximation and radiative effects

Nicolas Bilas (1) , Nicolas Pavloff (1)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

We consider the collision of a dark soliton with an obstacle in a quasi one dimensional Bose condensate. The variation of the soliton's shape and velocity during the collision are first determined within the adiabatic approach. In this framework, an "effective potential approximation" is established where the soliton behaves as an effective classical particle of mass twice the mass of a bare particle, evolving in an effective potential which is a convolution of the actual potential describing the obstacle. Radiative effects are then included within perturbation theory. The emitted waves form two counter propagating wave packets, both moving at the speed of sound. We determine, at leading order, the total amount of radiation emitted during the collision and compute the acceleration of the soliton due to the collisional process. It is found that the radiative process is quenched when the soliton's velocity reaches the velocity of sound in the system.

Mots clés: matter waves

Domaines: Mécanique statistique [cond-mat.stat-mech]; Formation de Structures et Solitons [nlin.PS]

Nicolas Bilas, Nicolas Pavloff. Dark soliton past a finite size obstacle: adiabatic approximation and radiative effects. 2005. ⟨hal-00003746v1⟩