We derive expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these moments for equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential, but require knowledge of equal time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moments to moments of spectral functions calculated from a variety of different approximations and use them to benchmark their accuracy.
Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics
最近在光晶格中的凝聚态模型的实验实现激发了对其非平衡行为的研究。基于有效BCS哈密顿量，已经对配对相互作用突然猝灭后超导体的动力学进行了预测;然而，它们的实验验证需要沿着双重约束制备哈伯德模型的合适激发态：（i）充分非绝热的斜坡方案对于激发非平衡动力学是必要的，以及（ii）必须避免超过超导性的临界温度的过热。对于通常讨论的相互作用斜坡，相应的能量尺度没有明确的分离。在这里，我们表明，这两个条件的匹配被简化的超冷费米子系统的内在弛豫行为：对于一个特殊的例子，我们检查的线性斜坡的预热化的瞬态制度[M。Moeckel和S. Kehrein，Phys. Rev. Lett. 100，175702（2008）]在使用Keldysh微扰理论从突然切换到绝热切换的交叉下。的动量分布的实时分析表现出早期的能量弛豫和后来的热化散射事件的时间分离。对于长但有限的斜升时间，该间隔可能很大。在预热化制度的动量分布类似于零温度费米液体的能量插入的斜坡仍然位于高能量模式。因此，超冷费米子被证明对加热具有鲁棒性，这简化了光晶格中非平衡BCS动力学的观察。
Inhomogeneous spectral moment sum rules for the retarded Green function and self-energy of strongly correlated electrons or ultracold fermionic atoms in optical lattices
Dissipation-Selected Resonant Fronts in a Driven-Dissipative Bose-Hubbard Lattice
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Beijing Key Laboratory of Advanced Quantum Technology, Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院先进量子技术北京市重点实验室）；Hefei National Laboratory（合肥国家实验室）；Songshan Lake Materials Laboratory（松山湖材料实验室）
Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory
