二维超流绕过任意穿透性势垒的临界速度
Critical velocity of a two-dimensional superflow past a potential barrier of arbitrary penetrability
AI总结：
本文结合水力近似、速端曲线法与 Janzen-Rayleigh 展开，推导二维超流绕过宽圆形任意穿透性势垒的临界速度闭式解，并经全波动方程虚时间数值模拟验证。
摘要：
我们从理论上研究了二维超流体绕过宽静态势垒作无耗散运动的临界速度。圆形势垒为临界速度提供了一个全面的解析框架，我们利用水力近似、速端曲线法以及速度势的 Janzen-Rayleigh 展开导出了闭式表达式。结果表明，这些解析估计与对完整波动方程进行虚时间积分所得的数值结果高度吻合。与大多数现有研究不同，我们的研究既不局限于不可穿透势垒，也不局限于四次相互作用哈密顿量，从而能够对近期利用原子 Bose-Einstein 凝聚体和二维傍轴光超流体开展的实验进行真实建模。
英文摘要：
We theoretically investigate the critical velocity for dissipationless motion of a two-dimensional superfluid past a static potential barrier of large width. The circular-shaped barrier provides a comprehensive analytical framework for the critical speed, for which we derive closed-form expressions using the hydraulic approximation, the hodograph method, and Janzen-Rayleigh expansions of the velocity potential. These analytical estimates are shown to be in good agreement with the numerical results of an imaginary-time integration of the full wave equation. In contrast to most of the state of the art, our study is not restricted to an impenetrable potential barrier nor to a quartic interaction Hamiltonian, which enables realistic modeling of recent experiments with atomic Bose-Einstein condensates and paraxial superfluids of light in two dimensions.
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