论文标题
在一维斑点电位中相互作用的bose气体的定位景观
Localization landscape for interacting Bose gases in one-dimensional speckle potentials
论文作者
论文摘要
虽然在谐波电位中充分了解了超电玻色子气体的特性和形状，但在随机电位的情况下，它们仍然是未知的很大一部分。在这里，我们使用定位 - 地面理论（LL）理论来研究一维（1D）斑点电位中溶液对Gross-Pitaevskii方程（GPE）的特性。在有吸引力的相互作用的情况下，我们发现LL允许人们预测GPE基态（GS）的定位中心的位置。对于弱排斥的相互作用，我们指出，可以将准1D GPE的GS理解为有限数量的单粒子状态的叠加，可以通过利用LL来计算。对于中间排斥性相互作用，我们为GS引入了一种类似Thomas-Fermi的方法，该方法具有在平滑状态下，远远超出了涉及原始电位的通常近似值。此外，我们表明，在Lifshitz玻璃制度中，LL可以很好地估算颗粒密度和化学电位。我们的方法可以应用于具有有限范围相关性的任何正值随机电位，并可以推广到更高维度的系统。
While the properties and the shape of the ground state of a gas of ultracold bosons are well understood in harmonic potentials, they remain for a large part unknown in the case of random potentials. Here, we use the localization-landscape (LL) theory to study the properties of the solutions to the Gross-Pitaevskii equation (GPE) in one-dimensional (1D) speckle potentials. In the cases of attractive interactions, we find that the LL allows one to predict the position of the localization center of the ground state (GS) of the GPE. For weakly repulsive interactions, we point out that the GS of the quasi-1D GPE can be understood as a superposition of a finite number of single-particle states, which can be computed by exploiting the LL. For intermediate repulsive interactions, we introduce a Thomas-Fermi-like approach for the GS which holds in the smoothing regime, well beyond the usual approximation involving the original potential. Moreover, we show that, in the Lifshitz glass regime, the particle density and the chemical potential can be well estimated by the LL. Our approach can be applied to any positive-valued random potential endowed with finite-range correlations and can be generalized to higher-dimensional systems.
