Trombettoni A, Smerzi A, Bishop A R
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev Lett. 2002 Apr 29;88(17):173902. doi: 10.1103/PhysRevLett.88.173902. Epub 2002 Apr 15.
We study the discrete nonlinear Schrödinger equation (DNLS) in an annular geometry with on-site defects. The dynamics of a traveling plane-wave maps onto an effective nonrigid pendulum Hamiltonian. The different regimes include the complete reflection and refocusing of the initial wave, solitonic structures, and a superfluid state. In the superfluid regime, which occurs above a critical value of nonlinearity, a plane wave travels coherently through the randomly distributed defects. This superfluidity criterion for the DNLS is analogous to (yet very different from) the Landau superfluidity criteria in translationally invariant systems. Experimental implications for the physics of Bose-Einstein condensate gases trapped in optical potentials and of arrays of optical fibers are discussed.
我们研究了具有在位缺陷的环形几何结构中的离散非线性薛定谔方程（DNLS）。行波平面波的动力学映射到一个有效的非刚性摆哈密顿量上。不同的状态包括初始波的完全反射和重新聚焦、孤子结构以及超流态。在高于非线性临界值时出现的超流态中，平面波能相干地穿过随机分布的缺陷。DNLS的这种超流性判据类似于（但又非常不同于）平移不变系统中的朗道超流性判据。文中还讨论了对捕获在光学势中的玻色 - 爱因斯坦凝聚气体以及光纤阵列物理的实验意义。
