Superfluidity versus Disorder in the Discrete Nonlinear Schrödinger Equation

Details Superfluidity versus Disorder in the Discrete Nonlinear Schrödinger Equation Superfluidity versus Disorder in the Discrete Nonlinear Schrödinger Equation

2002-05-19

arxiv.org/abs/cond-mat/0205397v1

Phys. Rev. Lett. 88, 173902 (2002)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevLett.88.173902

We study the discrete nonlinear Schr\"odinger equation (DNLS) in an annular geometry with on-site defects. The dynamics of a traveling plane-wave maps onto an effective ''non-rigid 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.

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