Bose-Einstein Condensates in Rotating Traps and Optical ... - BEC

∆ n ( U / δ ) 1/2
1
0.8
0.6
0.4
0.2
11.3 Nonlinear propagation of sound signals 155
0
0 3 6 9 12 15
T p b / w
∆ φ / π
0.25
0
0 3 6 9 12 15
T p b / w
Figure 11.10: Results for the density and relative signal amplitudes ∆n and ∆φ obtained from
DNLS simulations for varying barrier parameters TP ,b,w(see Eq.(11.1)), tunnel coupling δ
and on-site interaction U (see Eq.(11.8)) with δ ≪ U/3.
This is in agreement with the behavior we find for ∆n in the first (linear) and even in the
second (shockwave) regime as summarized in Fig. 11.10. The first order approximation to
sin(φℓ±1/2) in φℓ±1/2 is valid for ∆φ