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arXiv 1006.3530quant-phcond-mat.othercond-mat.quant-gas
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非平衡动力学的最优含时格子模型

Optimal time-dependent lattice models for nonequilibrium dynamics

Kaspar Sakmann, Alexej I. Streltsov, Ofir E. Alon, Lorenz S. Cederbaum

摘要:

晶格模型在理论物理和凝聚态物理中有着丰富的应用。一般来说,晶格模型包含时间无关的跳跃和相互作用参数,这些参数来自于非相互作用问题的Wannier函数。在这里,我们提出了一个新的概念的基础上的时间相关的Wannier函数和变分原理,导致最佳的时间相关的晶格模型。作为一个应用,我们使用玻色-哈伯德模型与时间相关的Wannier函数研究淬火方案涉及更高的频带。我们发现在动力学中时间尺度的分离,并表明,在某些情况下,量子系统的多带非平衡动力学可以得到基本上在单带模型的成本。

英文摘要:

Lattice models are abundant in theoretical and condensed-matter physics. Generally, lattice models contain time-independent hopping and interaction parameters that are derived from the Wannier functions of the noninteracting problem. Here, we present a new concept based on time-dependent Wannier functions and the variational principle that leads to optimal time-dependent lattice models. As an application, we use the Bose-Hubbard model with time-dependent Wannier functions to study a quench scenario involving higher bands. We find a separation of times scales in the dynamics and show that under some circumstances the multi-band nonequilibrium dynamics of a quantum system can be obtained essentially at the cost of a single-band model.

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