Palpacelli S, Succi S
Dipartimento di Matematica, Università Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 2):066708. doi: 10.1103/PhysRevE.77.066708. Epub 2008 Jun 20.
The phenomenon of Anderson localization in expanding one-dimensional Bose-Einstein condensates is investigated by numerically solving the Gross-Pitaevskii equation with a random speckle potential. To this purpose, a quantum lattice Boltzmann (QLB) method is used, and compared with a standard Crank-Nicolson scheme. The QLB simulations show evidence of Anderson localization even for relatively low-energy condensates, with a healing length as large as one-tenth of the Thomas-Fermi length. Moreover, very long-time simulations, lasting up to 15 000 optical confinement periods, indicate that the Anderson localization degrades in time, although at a very slow pace. In particular, the inverse localization length is found to decay according to a t;{-1/3} law. This lends support to the idea that localized wave functions, although not strictly ground states, represent extremely long-lived metastable states of the expanding condensate.
通过对具有随机散斑势的格罗斯 - 皮塔耶夫斯基方程进行数值求解，研究了一维膨胀玻色 - 爱因斯坦凝聚体中的安德森局域化现象。为此，使用了一种量子晶格玻尔兹曼（QLB）方法，并与标准的克兰克 - 尼科尔森格式进行了比较。QLB模拟表明，即使对于能量相对较低的凝聚体，也存在安德森局域化的证据，其愈合长度高达托马斯 - 费米长度的十分之一。此外，持续长达15000个光学限制周期的非常长时间的模拟表明，安德森局域化会随时间退化，尽管速度非常缓慢。特别是，发现逆局域化长度根据(t^{-1/3})定律衰减。这支持了这样一种观点，即局域化波函数虽然不是严格的基态，但代表了膨胀凝聚体的极其长寿命的亚稳态。
