10.6084/m9.figshare.1012069.v1 M J Edmonds M Valiente P Öhberg Numerical solutions to equations (17) and (18) 2013 IOP Publishing nonrigid pendulum nonlinear Josephson equations figure show population oscillations 2013-06-24 00:00:00 article https://iop.figshare.com/articles/_Numerical_solutions_to_equations_a_href_http_iopscience_iop_org_0953_4075_46_13_134013_article_jpb4/1012069 <p><strong>Figure 1.</strong> Numerical solutions to equations (<a href="http://iopscience.iop.org/0953-4075/46/13/134013/article#jpb461793eqn17" target="_blank">17</a>) and (<a href="http://iopscience.iop.org/0953-4075/46/13/134013/article#jpb461793eqn18" target="_blank">18</a>). The population |<em>c<sub>l</sub></em>|<sup>2</sup>, |<em>c<sub>r</sub></em>|<sup>2</sup> and ∑<sub><em>i</em></sub>|<em>c<sub>i</sub></em>|<sup>2</sup> are given by the blue dashed line, solid red line and dashed black lines, respectively. (a) and (c) show the population oscillations for 2<em>U</em>/<em>J</em> = 10 and Γ<sub>1</sub>/<em>J</em> = 1, the insets in each figure show the current <em>J</em>(<em>t</em>) as a function of time. Both (a) and (b) have the initial conditions c_{l/r}(t=0)=1/\sqrt{2}. (b) and (d) are plotted for 2<em>U</em>/<em>J</em> = 1 and Γ<sub>1</sub>/<em>J</em> = 5. (c) and (d) have the initial conditions c_{l}(t=0)={\rm e}^{{\rm i}\pi /2}/\sqrt{2} and c_{r}(t=0)=1/\sqrt{2}. The units of time are /<em>J</em>.</p> <p><strong>Abstract</strong></p> <p>We investigate the coherent dynamics of a Bose–Einstein condensate in a double well, subject to a density-dependent gauge potential. Further, we derive the nonlinear Josephson equations that allow us to understand the many-body system in terms of a classical Hamiltonian that describes the motion of a nonrigid pendulum with an initial angular offset. Finally we analyse the phase-space trajectories of the system, and describe how the self-trapping is affected by the presence of an interacting gauge potential.</p>