无序Gross-Pitaevskii晶格中激发的安德森局域化
Anderson localization of excitations in disordered Gross-Pitaevskii lattices
摘要：
我们研究的一维Gross-Pitaevskii晶格在零温度下存在的不相关的障碍。我们得到了基态场的热力学性质的解析表达式，并将它们与弱相互作用和强相互作用下的数值模拟进行了比较。我们分析了基态以上的弱激发，计算了Bogoliubov-de Gennes模的局域化性质。在长波长的限制，这些模式根据扩展的性质的基态离域。对于强相互作用，我们观察到并推导出在有限能量下，由于弱基态场涨落引起的有效关联无序，它们的局域化长度发散。我们推导出有效的强相互作用场方程的激发和推广到高维。
英文摘要：
We examine the one-dimensional Gross-Pitaevskii lattice at zero temperature in the presence of uncorrelated disorder. We obtain analytical expressions for the thermodynamic properties of the ground state field and compare them with numerical simulations both in the weak and strong interaction regimes. We analyze weak excitations above the ground state and compute the localization properties of Bogoliubov-de Gennes modes. In the long-wavelength limit, these modes delocalize in accordance with the extended nature of the ground state. For strong interactions, we observe and derive a divergence of their localization length at finite energy due to an effective correlated disorder induced by the weak ground state field fluctuations. We derive effective strong interaction field equations for the excitations and generalize to higher dimensions.
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